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Xiaomi Mi Band 6 review: Tried and tested formula is still a winner
By Andy Boxall April 27, 2021
Score Details
DT Recommended Product
"The Xiaomi Mi Band 6 is packed with sensors to track your activity, simple software to make it easy to use, and a comfortable fit for 24-hour wearability. It's not for the seriously sporty, but it's great for everyone else."
Easy to use with a reliable app
Comprehensive sensor array
Heart rate sensor accuracy concerns
The Xiaomi Mi Band, or Mi Smart Band as it's often known, has always been one of the best low-cost fitness bands available. Ever since the first one became available in 2015, Xiaomi has steadily updated it annually to keep up with new tech developments and it has only got better. The latest version is the Mi Band 6, which I've been wearing for more than a week now, and the formula hasn't changed much.
Software and battery life
It filled the space left by the Honor Band 6, another low-cost fitness tracker that surprised me with its ability and style, meaning that although there's plenty of goodwill towards the Mi Band 6, it still had a tough job ahead of it. Does Xiaomi's tried and tested wearable still succeed when others are edging more towards a smartwatch-like design? Here's how it did.
Xiaomi hasn't dared to be different with the Mi Band 6's looks, so it's very similar to the Mi Band 5 — a generously sized screen on a core module, attached to a silicone band with a pin-and-hole fitting to keep it on your wrist. It weighs barely anything at about 13 grams, is just over 12mm thick, and in the black color scheme here, is an almost completely incognito piece of tech. The module can pop out of the band so you can swap it for brighter versions if you want the Mi Band 6 to stand out a little more.
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Andy Boxall/Digital Trends
The screen is a 1.56-inch AMOLED panel, up from the 1.1-inch AMOLED on the Mi Band 5, and it's sharp, colorful, and bright. I've been able to glance and see it in all lighting conditions, although there's no auto-brightness feature, so I've just left it set to maximum. Sadly it's not an always-on screen, but you can set the amount of time the screen stays on (up to 10 seconds) and the raise-to-wake gesture is accurate and doesn't require excessive movement to activate.
You have the choice of hundreds of different watch faces through the app, but don't think this means you're spoiled for choice. There isn't much variation between them, and many are fairly unattractive. I struggled to find even a handful that I liked. I settled on one, and haven't had any wish to change it for another.
I've found it to be very comfortable, and have had no issue wearing it 24 hours a day. The pin-and-hole fitting can sometimes be awkward, but it's easy to do up here, plus there are masses of adjustments, so it'll fit regardless of how thick your wrist is. It doesn't get too sweaty, isn't annoying at night, and the band itself hasn't collected fluff either, so it'll keep looking neat and new for longer.
No, the Mi Band 6 isn't a style icon, but there's a reason Xiaomi hasn't deviated far from the Mi Band's established look — because it works. Smartwatch-like fitness bands are fine, but there's still space for a more compact, less intrusive fitness band that could be worn alongside a traditional watch. If you want a fitness tracker that fits well, is designed to be worn all day and night, is equipped with a pretty screen but isn't trying to be a smartwatch, this is it. It's also far better looking than the many cheap smartwatches that infest Amazon's wearable section, and a much better option overall.
Before going into detail, let's talk about the app. I've been using the Mi Band 6 with an iPhone 12 Pro. Xiaomi's app, called Xiaomi Wear, is available from the App Store. However, the band also works with the Mi Fit app, which is developed by Huami, the company behind the Amazfit range of wearables, and manufacturer of Xiaomi's wearables. Both integrate with Apple Health, but it's the Mi Fit app that I'd recommend using.
Confusing, right? Yes, especially because Mi Fit — the app not developed by Xiaomi — is the better option, because Xiaomi Wear hasn't been completely localized for use outside China and there are still a few options and menus in Chinese. Mi Fit may not be that attractive to look at, but it contains all the information you need, stays connected without issue, and won't put newcomers off.
Let's move on to the activity tracking. The band has 30 different workout modes, six of which can be automatically detected, or quickly activated in the menu. The usual options including walking, running, and swimming are there, plus a range of more unusual activities like street dance, Zumba, and boxing. I found the auto-detection to be a little haphazard, so ended up starting the workouts myself.
Mi Fit app walking Andy Boxall/Digital Trends
Mi Fit app sleep Andy Boxall/Digital Trends
Mi Fit app activity Andy Boxall/Digital Trends
Xiaomi Wear app Andy Boxall/Digital Trends
The data collected in the app is visualized nicely, with graphs showing heart rate, pace, and heart rate zones, along with GPS routing if you provide the app access. The simplicity is repeated throughout, with everything from sleep to stress data illustrated logically and clearly, but sometimes menus can be quite dense and historical data hard to find. The main screen in the Mi Fit app shows stats to do with the band, including battery remaining.
It does take some learning, and doesn't look as graphically modern as the Xiaomi Wear app, but it provides all the information you need in one place, and syncs reliably too. It also provides a PAI score, and the helpfulness of this statistic increases the longer you wear the band, but requires some reading into what it actually means as the in-app explanations are quite poor.
Xiaomi Mi Band 6 heart rate Andy Boxall/Digital Trends
Xiaomi Mi Band 6 SpO2 Andy Boxall/Digital Trends
How about the accuracy? During daily activity steps and calorie burn were consistent with my Apple Watch, as were SpO2 blood oxygen measurements. However, heart rate accuracy is less certain. During exercise and when monitoring in the background, it tends to give a higher reading. This may be a consequence of the fastening of the strap, as it's not easy or comfortable to get the pin-and-hole system really tight against your wrist. When you force a heart rate measurement the results are consistent with the Apple Watch at rest, showing there are some issues with the way it measures.
For sleep, I compared it to the under-mattress Withings Sleep Analyzer. It measured a very similar total sleep time and REM sleep, but under-estimated my deep sleep stage, and overestimated my light sleep stage compared to the Withings, both by about an hour. It shows a sleep score, and assesses breathing while asleep too. The sleep stage discrepancy isn't a concern, as it's not certain the Withings Sleep is 100% accurate either. However, the breathing measurements didn't line up with the Withings, which again may be to do with wearing the band loosely at night. Otherwise, for general use by someone without specific sleep issues, the Mi Band 6 is a good sleep tracking partner.
the Mi Band 6's activity tracking is excellent — comprehensive, easy to use, and logically presented for easy understanding
Other features include cycle tracking for women, breathing exercises, alerts to remind you to move around, and automatic stroke recognition when swimming. I had problems with the auto-pause feature, which seemed to pause workouts when I was still in the middle of it, forcing me to dig into the settings and turn the function off.
A software update may cure the slight overestimation of the heart rate sensor and some of the other accuracy concerns, but the rest of the Mi Band 6's activity tracking is excellent — comprehensive enough for the casual fitness fan, easy to use, and logically presented for easy understanding.
The Mi Band 6 is easy to use. Swipe up on the screen to show a vertical scrolling list of options, which includes workout modes and notifications, plus features like alarms and a world clock, and access to the heart rate monitor, stress monitor, and the SpO2 blood oxygen test. The order of the list can be changed in the app, as can features accessed with a side swipe, helping personalize the Mi Band 6. It's all relatively smooth and once the features have been placed in an order suitable for your own use, it's very convenient to live with.
The band shows notifications from your phone with moderate regularity, with most, but not all, alerts showing on your wrist. It seemed to have a problem showing Gmail notifications, for example, but not with Twitter or Outlook. It may be down to settings in iOS, but I couldn't seem to solve it. It's a nice addition, but don't expect alerts to be that helpful, as long messages don't show in their entirety, and there's no way to interact with them.
Xiaomi claims the battery will last for two weeks before it needs a recharge, but this will depend on your own use. If you want to take advantage of the continuous monitoring features for heart and stress, track sleep, and record a workout each day, it will last half this amount of time. My use with all these features active saw the battery at 8% on day seven. Recharging is quick, but is done with a short proprietary cable which is small and easy to lose.
The Mi Band 6 costs 40 British pounds, which is around $55. It's available through Xiaomi's online store in the U.K. Anyone in the U.S. will have to import one, although the Mi Band 6 will find its way onto Amazon, just like the Mi Band 5. One thing to note is to secure the U.K. or "global" version, otherwise it will include some China-specific features that won't work.
The Mi Band 6 is an excellent fitness band for people interested in their overall health, and who want to track their everyday movements and make improvements. I word it this way because the Mi Band 6 is not a serious fitness tracker for sports addicts. It doesn't have GPS built in, for example, and the accuracy concerns mean anyone seriously looking to improve their performance may find it inadequate.
This is all reflected in the price. High-end fitness tracking products, like the Suunto 7 or Garmin Forerunner 745, cost $500 or more, and are far better suited to people who are training for a marathon, or are seriously into a very specific activity. If that's not you, then spending so much is a bit pointless, and the Xiaomi Mi Band 6 is a great value when you consider what it can do, and the sensors it contains.
Xiaomi hasn't broken its tried-and-tested formula with the Mi Band 6, it remains a cheap, comfortable fitness band with a list of focused activity features, and all the crucial sensors a modern tracker needs to satisfy most people.
Is there a better alternative?
Samsung's Galaxy Fit 2 costs $60, has a similar design, and is more readily available, but it doesn't have an SpO2 sensor for improved sleep tracking, or GPS either. The Honor Band 6 is a good alternative if you prefer a larger screen and a more traditional clasp-style band. If Fitbit is your brand of choice, the Fitbit Charge 4 is our recommended version but at $150 it's a lot more expensive. Sometimes there are decent deals to lower this price a little though.
The Mi Band 6 should be hardwearing due to its simple plastic construction and being encased in the protective strap, which can be cheaply replaced if it breaks. The whole band has 5ATM (50 meters) water resistance so it's suitable for swimming but not for diving. Provided Xiaomi maintains app support (both versions had been updated within the last two weeks when writing this review) the Mi Band 6 will last for several years without issue.
Should you buy one?
Yes. It may require some effort or patience to secure one in the U.S., but it's a good fitness tracker at a very sensible price.
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Adur Estuary Rspb Reserve Bed and Breakfast, Cheap Hotel and Guest House Accommodation
OS Grid Reference TQ215049 for 1 night from Mon Jan 20, 2020 to Tue Jan 21, 2020 within 25 miles, in an Average Nightly price range of £1 to £200.
The New Sussex Hotel
Lancing 2.2 3.55 3 £103.25 £103.25 £103.25 £89.60 £89.60 £89.60 £89.60 £103.25
The Gather Inn
Brighton & Hove 3.33 5.36 N/A £41.00 £39.00 £37.00 £37.00 £37.00 £38.00 £60.00 £41.00
Olinda Guest House
Worthing 3.61 5.81 4 £30.00 £30.00 £30.00 £30.00 £30.00 £30.00 £30.00 £30.00
The Windsor Hotel
Worthing 3.81 6.14 N/A £90.00 £90.00 £90.00 £80.00 £90.00 £90.00 £90.00 £90.00
Best Western Plus Old Tollgate Hotel
Steyning 3.96 6.38 3 £64.68 £80.10 £80.10 £80.10 £73.80 £73.80 £73.80 £64.68
Best Western Princes Marine Hotel
Brighton & Hove 4.14 6.65 3 £55.00 £65.00 £95.00 £62.10 £54.00 £58.50 £103.50 £55.00
Manor Guest House
The Chatsworth Hotel
Worthing 4.27 6.87 3 £62.40 £72.80 £72.80 £84.00 £72.80 £80.00 £112.80 £62.40
Seafield Seafront Apartments Brighton
Brighton & Hove 4.4 7.07 N/A £50.00 £55.00 £55.00 £55.00 £55.00 £105.00 £125.00 £50.00
Smart Sea View Brighton
Grand Victorian Hotel – RelaxInnz
Langfords Hotel
Brighton & Hove 4.63 7.45 3 £42.00 £42.00 £42.00 £37.00 £37.00 £37.00 £64.00 £42.00
Brighton & Hove 4.7 7.57 4 £80.00 £80.00 £80.00 £80.00 £80.00 £80.00 £80.00 £80.00
Albany Hotel
The Courtlands Hotel
Brunswick and Thorn Apartments
The Burlington
Worthing 4.91 7.9 4 £70.00 £70.00 £70.00 £70.00 £65.00 £65.00 £65.00 £70.00
Brunswick Square Hotel
The Southern Belle
Mercure Brighton Seafront Hotel
Miami Hotel
Brighton 5.35 8.61 N/A £25.00 £25.00 £25.00 £25.00 £25.00 £25.00 £25.00 £25.00
The Brighton Hotel
Baggies Backpackers
The Moreland
The Oriental - Guest House
Holiday Inn Brighton Seafront
182 South Street, Lancing, BN15 8AU
Distance:2.2 miles | Star Rating:
Just off the seafront in Lancing, The New Sussex Hotel offers en suite accommodation alongside a pub, restaurant and beer garden. Elegantly styled rooms have free Wi-Fi, and the menu features a range ...more
Just off the seafront in Lancing, The New Sussex Hotel offers en suite accommodation alongside a pub, restaurant and beer garden. Elegantly styled rooms have free Wi-Fi, and the menu features a range of British favourites and local ales. Each guest room at The New Sussex Hotel has en suite bathroom facilities with shower or bath. There is a TV with DVD player, hairdryer and tea and coffee facilities. The restaurant serves gourmet burgers, steaks and sharing platters, and a selection of light meals at lunchtime. There are vegetarian choices including asparagus and mushroom risotto, vegetable chilli and Ploughman's lunch. Special dietary requirements can be catered for prior request. On the West Sussex coast, Lancing lies around 11 miles from the vibrant city of Brighton, and 3 miles from Worthing. The cathedral city of Chichester is around 40 minutes' drive, and the town is less than 2 miles from the picturesque South Downs region.
£103.25 £103.25 £103.25 £89.60 £89.60 £89.60 £89.60
330 Kingsway, Brighton & Hove, BN3 4LW
On the Brighton and Hove seafront, The Gather Inn is a fun place to eat, drink and stay. The property is located just 2 miles from Brighton city centre and overlooks Hove lagoon. The Gather Inn benefi ...more
On the Brighton and Hove seafront, The Gather Inn is a fun place to eat, drink and stay. The property is located just 2 miles from Brighton city centre and overlooks Hove lagoon. The Gather Inn benefits from limited free on-street parking in surrounding roads. There are 15 rooms, 11 of which are en-suite. All rooms have a plasma TV with Freeview channels and tea/coffee making facilities. Rooms are booked on a room-only basis, but breakfast can be purchased from the breakfast/brunch menu. The menu offers a good selection of options, including vegetarian, vegan and gluten free. The Gather Inn also has 2 bars. The Sea View Bar with restaurant is located on the top level, offering views over the lagoon and seafront. On the lower level you will find the Patio Bar, which is open in the warmer months. The Patio Bar features a raised dining area with views across the lagoon, an outdoor patio area, plasma TVs and a children's seating area with games. At the Gather Inn you will find locally sourced, homemade food with many options on the menu. The bars offer a selection of wines, cocktails, real ales, craft beers, lagers and ciders. Guests benefit from various special offers and discounts. Brighton Train Station is a 12-minute drive from The Gather Inn. Brighton Pier can be reached in 30 minutes by public transport.
199 Brighton Road, Worthing, BN11 2EX
The Olinda is a small friendly guesthouse with 3 letting rooms: 1 en suite double and 2 standard singles. All have free wireless internet access. We are located on the Worthing seafront, an easy 15 mi ...more
The Olinda is a small friendly guesthouse with 3 letting rooms: 1 en suite double and 2 standard singles. All have free wireless internet access. We are located on the Worthing seafront, an easy 15 minute walk from the town centre. Parking on road.
12-20 Windsor Road, Worthing, BN11 2LX
The Windsor Hotel is set in Worthing and features a garden and a terrace. Featuring a restaurant, the property also has a bar. The accommodation features free WiFi. Continental and buffet breakfast op ...more
The Windsor Hotel is set in Worthing and features a garden and a terrace. Featuring a restaurant, the property also has a bar. The accommodation features free WiFi. Continental and buffet breakfast options are available every morning at the hotel. Brighton & Hove is 18 km from The Windsor Hotel. Gatwick Airport is 53 km away.
The Moorings, 4 Selden Road, Worthing, BN11 2LL
The Moorings in Selden Road Worthing just off the A259 Brighton Road and is one of the AA's 25 Friendliest Landladies in the UK Awarded 2011 and also has a Gold award for Green Tourism Worthing is ...more
The Moorings in Selden Road Worthing just off the A259 Brighton Road and is one of the AA's 25 Friendliest Landladies in the UK Awarded 2011 and also has a Gold award for Green Tourism Worthing is situated on the coast between Brighton and Chichester and is an ideal centre for touring & business. Easy access to the South Downs National Park London and Portsmouth. When making your on line bookling - please let us know what time you will be arriving so we know to be here to welcome you
The Street, Bramber, Steyning, BN44 3WE
Situated in the quaint village of Bramber at the foot of the South Downs, The Best Western Old Tollgate Hotel & Restaurant offers free parking, free Wi-Fi and a traditional carvery restaurant. The spa ...more
Situated in the quaint village of Bramber at the foot of the South Downs, The Best Western Old Tollgate Hotel & Restaurant offers free parking, free Wi-Fi and a traditional carvery restaurant. The spacious bedrooms at Old Tollgate Hotel each have a private bathroom and tea/coffee facilities. Rooms also feature a flat-screen TV with satellite channels, a hairdryer and trouser press. The Carvery Restaurant serves traditional British cuisine, and features original fireplaces and exposed beams. The cosy bar offers beverages and snacks, and tasty breakfasts are served daily. Just outside Steyning, The Best Western Old Tollgate Hotel is a 20-minute drive from Brighton and Hove. Surrounded by West Sussex countryside, there are many popular walks and cycle tracks nearby.
153 Kingsway, Brighton & Hove, BN3 4GR
Situated on Brighton Seafront, Best Western Princes Marine Hotel has a traditional restaurant and views across the English Channel. There is limited private parking, free fibre optic WiFi and a 24-hou ...more
Situated on Brighton Seafront, Best Western Princes Marine Hotel has a traditional restaurant and views across the English Channel. There is limited private parking, free fibre optic WiFi and a 24-hour front desk. The bright and airy bedrooms at Princes Marine Hotel each have a cosy seating area and a private modern bathroom. Rooms also feature a TV and tea/coffee facilities, and some have sea views. A hearty breakfast buffet is served daily in the spacious restaurant, which also offers a varied bistro menu for evening dining. The Kingsway Bar offers a range of light snacks and beverages. Best Western Princes Marine is a 25-minute stroll along the seafront from Brighton's vibrant centre. The famous Brighton Pier is 2 miles away, and Hove Lagoon is just half a mile away.
100 Broadwater Road, Worthing, BN14 8AN
Conveniently situated for touring the south coast, leisure, or business. Close to Worthing town and the station. Good access to the South Downs, villages and local towns including Brighton, Chichester ...more
Conveniently situated for touring the south coast, leisure, or business. Close to Worthing town and the station. Good access to the South Downs, villages and local towns including Brighton, Chichester, Arundel, Goodwood, Findon, Steyning and Shoreham
The Steyne, Worthing, BN11 3DU
Superbly situated for Worthing town centre, 19th-century Chatsworth Hotel is a family-run, Grade II Listed building with Georgian frontage overlooking Steyne Gardens. The hotel is conveniently near th ...more
Superbly situated for Worthing town centre, 19th-century Chatsworth Hotel is a family-run, Grade II Listed building with Georgian frontage overlooking Steyne Gardens. The hotel is conveniently near the seafront. Each classically furnished room has en suite facilities, free Wi-Fi internet access and a Freeview TV. Leisure facilities include a games room with 2 full-size snooker tables, a pool table and table tennis. Hardwick Restaurant serves good cuisine, using local produce, in a welcoming atmosphere. Guests may also enjoy a drink or snack in the Chatsworth lounge and cocktail bars. From reception, you can purchase vouchers for on-street parking. There is also a public car park a 5-minute walk away, where guests can enjoy a discounted rate.
10 Seafield Road, Brighton & Hove, BN3 2TN
Distance:4.4 miles | Star Rating: N/A
Quietly set on a beautiful tree-lined road in Brighton and Hove, the Seafield Seafront Apartments Brighton offers accommodation with free WiFi access and shared kitchen facilities. The seafront is wit ...more
Quietly set on a beautiful tree-lined road in Brighton and Hove, the Seafield Seafront Apartments Brighton offers accommodation with free WiFi access and shared kitchen facilities. The seafront is within 100 metres. The studio apartments are cleverly designed to provide a compact living and sleeping area, with a flat-screen TV, a double sofa bed, and tea and coffee making facilities. Each apartment also offers a raised mezzanine deck with a double bed and a private shower room with complimentary toiletries. The Seafield Seafront Apartments Brighton have a kitchen and dining area, with a microwave, oven, and a toaster. Essential kitchenware is also provided and there is a convenient vending machine in the reception area. The apartments include tea and coffee making facilities. Hove Station is just 4 minutes' drive or 15 minutes' walk from the Seafield Seafront Apartments Brighton and Churchill Square Shopping Centre is within a 30-minute walk. There are many independent boutique stores, bars, and countless restaurants within a 10-minute stroll of the apartments.
9-12 St Catherines Terrace, Brighton & Hove, BN3 2RZ
The Smart Sea Brighton View is 100 from the beach and a 10-minute walk from Hove Train Station. It offers affordable accommodation and a 24-hour internet café with free Wi-Fi. The hostel, which dates ...more
The Smart Sea Brighton View is 100 from the beach and a 10-minute walk from Hove Train Station. It offers affordable accommodation and a 24-hour internet café with free Wi-Fi. The hostel, which dates back from 1905, provides both private rooms and shared dormitories. All have access to bathroom facilities, and some rooms have spectacular sea views. Hove Cricket Ground is just a 5-minute cycle away. Brighton Pier and the Royal Pavilion are less than 2 miles away.
27 Railway Approach, Worthing, BN11 1UR
Directly opposite Worthing Train Station, this traditional hotel from the late 19th century has a restaurant, bar and comfy rooms. Worthing seafront is 15 minutes' walk away via the town centre. The G ...more
Directly opposite Worthing Train Station, this traditional hotel from the late 19th century has a restaurant, bar and comfy rooms. Worthing seafront is 15 minutes' walk away via the town centre. The Grand Victorian has a period bar serving Real Ale, and a conservatory restaurant overlooking a garden area with seating. Breakfast consists of cooked and continental items. Each pleasant bedroom has a bathroom, flat-screen TV with many channels, and tea and coffee facilities. There is free Wi-Fi in public areas of the hotel. Worthing Station has good train links to London Victoria, Chichester and Brighton.
Third Avenue, Brighton & Hove, BN3 2PX
Situated on a tree-lined avenue, Langfords Hotel is just a few metres from the shingle beach of Brighton & Hove's historical seafront. The shops and restaurants of Brighton's city centre can be reache ...more
Situated on a tree-lined avenue, Langfords Hotel is just a few metres from the shingle beach of Brighton & Hove's historical seafront. The shops and restaurants of Brighton's city centre can be reached in a 15-minute walk. It has a lounge bar, a quiet garden and rooms with LCD TVs and free high-speed Wi-Fi. Brighton's famous Pier and historic Royal Pavilion are 15 minutes' bus journey from Langfords. A range of restaurants are within a 5-minute walk, and Hove Rail Station is less than a mile away. The rooms all have a telephone and free tea and coffee facilities. Private bathrooms in every room have free toiletries. On-street parking permits are available from reception, at an additional cost. The lounge bar is open until late and the bar has an LCD TV and access to the garden.
4 Shirley Road, Brighton & Hove, BN36NN
Charming house in a quiet road with free parking. Near Hove or Brighton Stations and Sussex Cricket Ground. Very comfortable pretty rooms and delicious breakfast.Television and tea-making in rooms. En ...more
Charming house in a quiet road with free parking. Near Hove or Brighton Stations and Sussex Cricket Ground. Very comfortable pretty rooms and delicious breakfast.Television and tea-making in rooms. Ensuite or private facilities. style=&quotdisplay:
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19-23 The Drive, Brighton & Hove, BN3 3JE
Providing free WiFi, Albany Hotel is located in Brighton & Hove, 1.4 km from Churchill Square Shopping Centre and an 18-minute walk from i360 Observation Tower. This 3-star hotel offers a 24-hour fron ...more
Providing free WiFi, Albany Hotel is located in Brighton & Hove, 1.4 km from Churchill Square Shopping Centre and an 18-minute walk from i360 Observation Tower. This 3-star hotel offers a 24-hour front desk. The property is a 20-minute walk from Victoria Gardens and 1.8 km from The Brighton Centre. At the hotel, the rooms include a desk, a wardrobe, a flat-screen TV and a private bathroom. Komedia is 2 km from Albany Hotel, while Brighton Dome is 2.2 km from the property. The nearest airport is Gatwick Airport, 37 km from the accommodation.
19/27 The Drive, Brighton & Hove, BN3 3JE
This Victorian hotel sits on a tree-lined avenue a 2-minute walk from the seafront. It has an award-winning table d'hôte restaurant and free WiFi. Each en suite room at The Courtlands Hotel has a fla ...more
This Victorian hotel sits on a tree-lined avenue a 2-minute walk from the seafront. It has an award-winning table d'hôte restaurant and free WiFi. Each en suite room at The Courtlands Hotel has a flat-screen TV and free toiletries. Guests can also enjoy facilities for making tea and coffee. Nick's Place restaurant serves European cuisine, afternoon teas and a traditional Sunday lunch. The bar opens until late and serves snacks. Courtlands is a 10-minute walk from Hove Rail Station and 1 mile from Brighton's Churchill Square Shopping Centre. A beach hut overlooking Brighton and Hove seafront is available for day hire.
Second Avenue, Brighton & Hove, BN3 2LL
Elegant, comfortable and stylish rooms combined with intuitive and discreet levels of customer care combine to give you the ultimate in an enhanced stay experience. Visit England has awarded us the ci ...more
Elegant, comfortable and stylish rooms combined with intuitive and discreet levels of customer care combine to give you the ultimate in an enhanced stay experience. Visit England has awarded us the city's first 5 star grading for guest accommodation and we are also licensed for civil partnerships and weddings. Housed in a Victorian Villa with a hidden walled garden all our en-suite rooms amaze and delight our guests through a combination of traditional features and individual design. Visit England has given the Claremont a Best Breakfast award
First Avenue, Brighton & Hove, BN3 2GU
The Imperial Hotel is within a 3-minute walk from the promenade, Hove Lawns and the beach. The hotel is set in a Regency period building with high ceilings, a terrace, a spacious bar, a breakfast room ...more
The Imperial Hotel is within a 3-minute walk from the promenade, Hove Lawns and the beach. The hotel is set in a Regency period building with high ceilings, a terrace, a spacious bar, a breakfast room and a lounge. There is free Wi-Fi available throughout the property. The Imperial Hotels offers rooms with a flat-screen TV and tea/coffee making facilities. Some rooms have a sea view and all rooms come with a private bathroom and complimentary toiletries. At The Imperial Hotel you will find a 24-hour front desk. The hotel also offers meeting facilities, a shared lounge and luggage storage. A 20-minute walk along the seafront will bring you to Brighton's main attractions, including the Royal Pavillion, The Lanes, i360 Tower, Churchill Square Shopping Centre and Brighton Pier. Hove Station is around 1 mile away and other public transport options are available.
Brunswick and Thorn Thorn Road, Worthing, BN11 3ND
Located in Worthing, Brunswick and Thorn Apartments provides accommodation with free WiFi and seating area. Each unit comes with an oven, microwave, a coffee machine, as well as a toaster and kettle. ...more
Located in Worthing, Brunswick and Thorn Apartments provides accommodation with free WiFi and seating area. Each unit comes with an oven, microwave, a coffee machine, as well as a toaster and kettle. There is also a kitchen equipped with a fridge. Guests can grab a bite to eat in the on-site restaurant, which serves a variety of British dishes. Snorkelling and windsurfing are possible within the area, and the apartment offers water sports facilities. Brighton & Hove is 21 km from Brunswick and Thorn Apartments. The nearest airport is Gatwick Airport, 60 km from the property.
Marine Parade, Worthing, BN11 3QL
Opposite Worthing Beach, this refurbished seafront property with a Victorian style dates from 1865. Enjoy full English breakfasts, sea views and Italian food in bustling Gio's Bar. The Burlington over ...more
Opposite Worthing Beach, this refurbished seafront property with a Victorian style dates from 1865. Enjoy full English breakfasts, sea views and Italian food in bustling Gio's Bar. The Burlington overlooks the promenade and is about 10 minutes' walk from Worthing town centre. Worthing Pier and Pavilion Theatre are about 5 minutes' walk away. Spacious rooms have high ceilings and tea/coffee facilities. Victorian features blend with a modern décor, and some rooms have a sea view. Each room has its own bathroom. Gio's Bar opens daily, and stays open until 02:00 on Fridays and Saturdays.
11 Brunswick Square, Brighton & Hove, BN3 1EH
The Brunswick Square Hotel offers a superb base in the most elegant Grade I listed square in Brighton and Hove, moments from the beach and close to all that Brighton and Hove have to offer. All the Br ...more
The Brunswick Square Hotel offers a superb base in the most elegant Grade I listed square in Brighton and Hove, moments from the beach and close to all that Brighton and Hove have to offer. All the Brunswick rooms are en suite and have free Wi-Fi . The Brunswick also has 4 poster rooms and Master Rooms with sea view. A continental and full English breakfast are available (for a small extra charge) in the stylish dining room, with views over the square and to the sea. All children under 12 years old eat breakfast for free.
3 Waterloo Street, Brighton & Hove, BN3 1AQ
The Southern Belle is a 19th-century pub and hotel which also features a traditional bar on-site, offering accommodation adjacent to the Brighton seafront. The light, spacious rooms at The Southern Be ...more
The Southern Belle is a 19th-century pub and hotel which also features a traditional bar on-site, offering accommodation adjacent to the Brighton seafront. The light, spacious rooms at The Southern Belle include TVs and tea/coffee-making facilities. Some rooms offer a partial sea view. The relaxing bar features an open fireplace and comfortable sofas. It serves real ales, a range of wines and spirits, as well as offering a food menu. There is also a micro-theatre which hots a variety of shows. A Continental buffet breakfast is included. The i360 Observation Tower is a 7-minute walk from The Southern Belle. Hove or Brighton Rail Station are both just 5 minutes' drive away from The Southern Belle. Both the spectacular Brighton Royal Pavilion and Brighton Pier are 20 minutes' walk away.
149 Kings Road, Brighton & Hove, BN1 2PP
This elegant Victorian hotel overlooks the beach, sea and promenade, and has a brasserie restaurant for guests to enjoy. It is half a mile from Churchill Square shopping centre, and has free high-spee ...more
This elegant Victorian hotel overlooks the beach, sea and promenade, and has a brasserie restaurant for guests to enjoy. It is half a mile from Churchill Square shopping centre, and has free high-speed Wi-Fi throughout. Mercure Brighton Seafront Hotel has a bar and 24-hour room service. Each clean, modern room has a flat-screen TV with satellite channels and an en suite bathroom with toiletries. Some rooms have sea views. A Grade II Listed building, it was built in 1864 and retains traditional features like its original Regency staircase. Guests can dine in the restaurant, which overlooks the sea and offers food 24 hours a day. Brighton Pier, The Lanes and the Royal Pavilion are 1 mile from the hotel. The convention centre and town centre can be reached in around 10 minutes on foot.
22 bedford square, Brighton, BN1 2PL
The Miami Hotel is a grade 2 listed double regency town house sitting in the middle of a quiet landscaped seafront square.There are 25 bedrooms accommodating one to four persons, many having the lu ...more
The Miami Hotel is a grade 2 listed double regency town house sitting in the middle of a quiet landscaped seafront square.There are 25 bedrooms accommodating one to four persons, many having the luxury of direct sea views. Unbeatable value and location
143-145 Kings Road, Brighton & Hove, BN1 2PQ
On Brighton's seafront promenade, this hotel offers elegant interiors and scenic sea views, 15 minutes' walk from the Royal Pavilion. Cooked breakfasts are served, and free WiFi is available. Bright a ...more
On Brighton's seafront promenade, this hotel offers elegant interiors and scenic sea views, 15 minutes' walk from the Royal Pavilion. Cooked breakfasts are served, and free WiFi is available. Bright and warmly furnished, each room includes a private bathroom with a hairdryer. Rooms include a TV, ironing facilities, and tea and coffee. Some rooms also offer lovely sea views. Brighton Rail Station and the boutique shops of Brighton Lanes can be reached in a 15-minute walk. Brighton Pier is 20 minutes away on foot, while Brighton's central shops, clubs and restaurants are 15 minutes' walk away. Breakfast options range from a full English to pancake stacks, yoghurt, berries and homemade granola. There is charged parking in front of the hotel and it is based on a first come first served policy. Guests can only book spaces on arrival.
33 Oriental Place, Brighton & Hove, BN1 2LL
A grade II listed building just 2 minutes' walk from the beach, Baggies Backpackers is located in seaside town of Brighton & Hove. With free WiFi access in public areas, The Brighton Centre is 10 minu ...more
A grade II listed building just 2 minutes' walk from the beach, Baggies Backpackers is located in seaside town of Brighton & Hove. With free WiFi access in public areas, The Brighton Centre is 10 minutes' walk away and the famous Lanes are a 17-minute journey on foot. With either a sea view or a view of the town, each room benefits from shared bathroom facilities. At Baggies Backpackers there is a shared kitchen. Other facilities offered at the property include a shared lounge, a games room and luggage storage. The hostel is a mile from Brighton Pier and SEA LIFE Brighton. The Royal Pavilion is 17 minutes' walk, and Brighton Train Station is a 6-minute drive from Baggies Backpackers.
33 Montpelier Road, Brighton, BN1 2LQ
Come join us at The Moreland, a wonderfully contemporary Brighton bed and breakfast, where a warm welcome is assured. Our b&ampampampampampb is in a residential side street, minutes from the main High ...more
Come join us at The Moreland, a wonderfully contemporary Brighton bed and breakfast, where a warm welcome is assured. Our b&ampampampampampb is in a residential side street, minutes from the main High Street and everything that is Brighton.
139 - 141 Kings Road, Brighton & Hove, BN1 2NA
Situated in central Brighton and with views of the seafront, this magnificent Grade II Listed building overlooks the West Pier and offers free Wi-Fi. The rail station is a 15-minute walk from Kings Ho ...more
Situated in central Brighton and with views of the seafront, this magnificent Grade II Listed building overlooks the West Pier and offers free Wi-Fi. The rail station is a 15-minute walk from Kings Hotel. A wide-ranging breakfast menu is available at Kings Hotel, including pancakes with fresh berries and maple syrup, grilled or poached fish, and a full English breakfast. The K Bar has a wide selection of drinks available along with a limited snack menu. All rooms are en-suite and many have scenic sea views. Each room features a flat-screen TV with satellite channels, hairdryer and hospitality tray. Situated just metres from the beach, the Kings Hotel is a mile from Brighton Pier. Local attractions including the Brighton Centre, Brighton Pier, Royal Pavilion and the Sealife Centre can be reached in 20 minutes' walk.
9 Oriental Place, Brighton & Hove, BN1 2LJ
Situated 50 metres from the beach, The Oriental is 5 minutes' walk from Brighton's city centre. Gatwick Airport is less than half an hour by car or train, and London is only 50 minutes away by train. ...more
Situated 50 metres from the beach, The Oriental is 5 minutes' walk from Brighton's city centre. Gatwick Airport is less than half an hour by car or train, and London is only 50 minutes away by train. The stylish rooms boast a contemporary décor, an en suite bathroom with luxury toiletries, a flat-screen TV, free Wi-Fi, and tea/coffee making facilities. Some rooms also feature a seating area with a luxurious sofa, and a work desk. Guests can enjoy a hearty, freshly cooked Full English breakfast or a continental option, served daily. Vegetarian and special dietary requirements are also catered for. Conveniently located, The Oriental is less than 5 minutes' walk away from notorious attractions such as The Royal Pavilion, Brighton Conference Centre and the Lanes.
137 Kings Rd, Brighton & Hove, BN1 2JF
Located on the vibrant Brighton seafront, the Holiday Inn Brighton Seafront offers breathtaking sea-facing bedrooms with air conditioning. The hotel boasts the Open Lobby bar and restaurant with a ter ...more
Located on the vibrant Brighton seafront, the Holiday Inn Brighton Seafront offers breathtaking sea-facing bedrooms with air conditioning. The hotel boasts the Open Lobby bar and restaurant with a terrace that has uninterrupted views of the beach, sea and horizon. The recently refurbished, airy rooms include satellite TV with pay-per-view movies, and a private bathroom with toiletries and a hairdryer. Guests can make use of a work desk with a lamp, tea/coffee facilities, and 24-hour room service. Holiday Inn Brighton Seafront is a 15-minute walk from Brighton Dome and Brighton Lanes for shops, bars and restaurants. The Brighton Centre is a 2-minute walk away, and Gatwick Airport can be reached in 40 minutes by car. With a contemporary dining atmosphere and a terrace overlooking the sea, the Stock Burger Co Restaurant serves gourmet burgers and craft beer. During the summer months, guests can explore the exclusive terrace and soak up the sun whilst enjoying views of the British Airways I360.


text:
package org.thingsboard.server.common.data.kv;

import java.util.Objects;
import java.util.Optional;

public class BasicTsKvEntry implements TsKvEntry {
    private static final int MAX_CHARS_PER_DATA_POINT = 512;
    protected final long ts;
    private final KvEntry kv;

    public BasicTsKvEntry(long ts, KvEntry kv) {
        this.ts = ts;
        this.kv = kv;
    }

    @Override
    public String getKey() {
        return kv.getKey();
    }

    @Override
    public DataType getDataType() {
        return kv.getDataType();
    }

    @Override
    public Optional<String> getStrValue() {
        return kv.getStrValue();
    }

    @Override
    public Optional<Long> getLongValue() {
        return kv.getLongValue();
    }

    @Override
    public Optional<Boolean> getBooleanValue() {
        return kv.getBooleanValue();
    }

    @Override
    public Optional<Double> getDoubleValue() {
        return kv.getDoubleValue();
    }

    @Override
    public Optional<String> getJsonValue() {
        return kv.getJsonValue();
    }

    @Override
    public Object getValue() {
        return kv.getValue();
    }

    @Override
    public long getTs() {
        return ts;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (!(o instanceof BasicTsKvEntry)) return false;
        BasicTsKvEntry that = (BasicTsKvEntry) o;
        return getTs() == that.getTs() &&
                Objects.equals(kv, that.kv);
    }

    @Override
    public int hashCode() {
        return Objects.hash(getTs(), kv);
    }

    @Override
    public String toString() {
        return "BasicTsKvEntry{" +
                "ts=" + ts +
                ", kv=" + kv +
                '}';
    }

    @Override
    public String getValueAsString() {
        return kv.getValueAsString();
    }

    @Override
    public int getDataPoints() {
        int length;
        switch (getDataType()) {
            case STRING:
                length = getStrValue().get().length();
                break;
            case JSON:
                length = getJsonValue().get().length();
                break;
            default:
                return 1;
        }
        return Math.max(1, (length + MAX_CHARS_PER_DATA_POINT - 1) / MAX_CHARS_PER_DATA_POINT);
    }

}

redpajama_set_name: RedPajamaGithub


text:
Cerro Paine Grande é um pico da Cordilheira dos Andes localizado no Chile.

Ver também
 Monte Fitz Roy
 Parque Nacional Los Glaciares

Montanhas do Chile

redpajama_set_name: RedPajamaWikipedia


text:
Oscilloscope Laboratories Acquires Jessie Barr's Teen Drama 'Sophie Jones'
By Dino-Ray Ramos
Dino-Ray Ramos
Associate Editor/Reporter
@DinoRay
More Stories By Dino-Ray
Timely 'MLK/FBI' And Stranger-Than-Fiction 'Assassins' Documentaries Debut – Specialty Preview
Ji-young Yoo Joins Apple And A24's 'The Sky Is Everywhere'
SXSW Sets 'Demi Lovato: Dancing With The Devil' As Film Festival Opener; Unveils Program Highlights
Courtesy of Oscilloscope Laboratories
EXCLUSIVE: Oscilloscope Laboratories is about to get angsty. The Adam Yauch indie film company has acquired North American rights to Jessie Barr's coming-of-age drama Sophie Jones executive produced by Nicole Holofcener. The film is slated to be released in the first quarter of 2021.
Inspired by true experiences of grief, girlhood, and growing up, Sophie Jones paints a portrait of the titular 16-year-old (played by the director's cousin Jessica Barr) who is shocked by the untimely death of her mother. As she struggles with her loss and the challenges of being a teen, Sophie tries everything she can to feel something again, while holding herself together.
"Sophie Jones has been a true labor of love and I'm beyond thrilled that the film has found its home with Oscilloscope," said Jessie Barr, who was also a Sundance Fellow. "This is a dream come true. Oscilloscope's love for filmmakers, commitment to creative collaboration, and passion for the film make me confident Sophie Jones will reach its audience. We can't wait to share it."
O-Scope's Aaron Katz added, "We are very excited to be bringing Sophie Jones to audiences. Jessie has crafted a heartfelt and honest coming-of-age portrait that reignited a range of teenage emotions I thought I had long since escaped. The film's naturalism and relatability provided an 80-minute escape to normalcy in what has undoubtedly been a hell of a year."
Sophie Jones made its World Premiere at the Festival du Cinéma Américain de Deauville 2020. The teen drama was written by Jessica Barr and Jessie Barr who also serve as producers alongside Joe Dinnen and Lindsay Guerrero. The executive producer is Nicole Holofcener.
The deal was negotiated with UTA Independent Film Group on behalf of the filmmakers. Barr is repped by Management 360.
This article was printed from	https://deadline.com/2021/01/oscilloscope-laboratories-jessie-barr-sophie-jones-nicole-holofcener-1234664817/


Kim Willoughby who was arrested and charged with assault pleaded not guilty. The volleyballer who went college at the U. of Hawaii won a silver medal at the Olympics.
She is alleged to have caused serious injury to Sara Daniel and surrendered to authorities after the indictment was sealed.
Willoughby's criminal attorney said that she had to defend herself in this situation and had no other choice but to use force in fighting back.
Sherri Chun who was identified as the Deputy City Prosecutor claimed that Willoughby followed Sara and that there was no self defense involved.
If this case happened in New York and it was a felony, a New York Criminal Lawyer would tell her, she would be potentially facing over a year in jail if convicted.
Hiring a New York Criminal Lawyer is essential for you if you are involved in this kind of case. A New York Criminal Lawyer will help you get the justice you deserve.
Daniel's lawyer said that her client was injured seriously and was in distress in the hospital.
The firm of Stephen Bilkis & Associates and its NY Criminal Defense Attorneys with several locations in the New York Metropolitan Area including Lynbrook New York can be of great help to you if you find yourself the target of a criminal action. Facing charges without knowledgeable professional representation could lead to disruptive results.


text:
Enhanced Stats
CMSV at The Sage Colleges
@ Albany, NY
College of Mt. St. Vincent
17 Sage Colleges
College of Mt. St. Vincent (6-5) 9 8 17
Sage Colleges (2-9) 2 3 5
-- 1st -- College of Mt. St. Vincent Sage Colleges
College of Mt. St. Vincent 26:50 Sophia Raccolin (Emma Dell'Aquila ) 1 0
Sage Colleges 24:23 Anne Risler (unassisted) 1 1
Sage Colleges 21:31 Brittany Gage (unassisted) 1 2
College of Mt. St. Vincent 14:40 Emma Dell'Aquila (Free position shot) 2 2
College of Mt. St. Vincent 13:08 Amy Cohen (unassisted) 3 2
College of Mt. St. Vincent 12:16 Paulina Mandujano (Caitlin Elia ) 4 2
College of Mt. St. Vincent 12:05 Emma Dell'Aquila (Caitlin Elia ) 5 2
College of Mt. St. Vincent 08:41 Emma Dell'Aquila (unassisted) 6 2
College of Mt. St. Vincent 06:00 Caitlin Elia (Free position shot) 7 2
College of Mt. St. Vincent 03:48 Emma Dell'Aquila (Morgan Pavlik ) 8 2
College of Mt. St. Vincent 01:23 Morgan Pavlik (unassisted) 9 2
-- 2nd -- College of Mt. St. Vincent Sage Colleges
College of Mt. St. Vincent 28:17 Sophia Raccolin (unassisted) 10 2
College of Mt. St. Vincent 27:54 Morgan Pavlik (Free position shot) 11 2
College of Mt. St. Vincent 27:29 Paulina Mandujano (Emma Dell'Aquila ) 12 2
College of Mt. St. Vincent 25:05 Kacey Brown (unassisted) 13 2
College of Mt. St. Vincent 18:23 UP - Sophia Raccolin (unassisted) 14 2
Sage Colleges 17:15 Anne Risler (unassisted) 14 3
Sage Colleges 14:50 Anne Risler (Brittany Gage ) 14 4
College of Mt. St. Vincent 12:46 Shannon Dalton (unassisted) 15 4
College of Mt. St. Vincent 11:22 Amy Cohen (unassisted) 16 4
Sage Colleges 07:55 Brittany Gage (unassisted) 16 5
1 Morgan Pavlik * m 2 1 2 2 4 6 2 2
5 Mia Peters 0 0 1 1 3 2 1 2
6 Paulina Mandujano * m 2 0 5 3 1 0 2 0
7 Amy Cohen 2 0 7 3 2 0 2 1
8 Caitlin Elia * m 1 2 5 3 3 7 3 1
9 Meghan Hoban * d 0 0 0 0 2 0 0 0
10 Kacey Brown * m 1 0 1 1 10 0 1 4
11 Erin Hughes 0 0 1 0 0 0 2 0
12 Emma Dell'Aquila * a 4 2 4 4 6 0 2 5
14 Veronica Sevivas * m 0 0 1 1 1 2 2 2
15 Shannon Dalton * a 1 0 3 2 2 0 2 0
16 Grace Barry * d 0 0 0 0 1 0 0 2
17 Teresa Geberth 0 0 0 0 1 0 0 0
19 Erin Bouvee * d 0 0 0 0 3 0 2 2
20 Ellexandrea Dahlke 0 0 0 0 0 0 0 1
22 Sophia Raccolin * m 4 0 7 6 3 0 0 1
23 Alexa Diaz 0 0 0 0 0 0 1 0
33 Allyson Weakliem * gk 0 0 0 0 1 0 1 0
33 Allyson Weakliem (W, 6-5)	 5 60:00 2 7
2 Naya Green 0 0 0 0 1 0 0 0
3 Kerry McKeown * d 0 0 0 0 2 0 2 2
5 Sophia Keravich * m 0 0 0 0 1 0 0 1
6 Anne Risler * a 3 0 5 3 2 4 4 1
7 Sophia Pierce * a 0 0 1 1 1 0 2 1
9 Chloe Pratt * m 0 0 0 0 1 0 2 0
10 Brittany Gage * m 2 1 4 3 6 0 1 1
11 Kelsey Fairley * m 0 0 1 0 2 0 6 2
13 Gabriela Cabrera 0 0 0 0 0 0 0 0
15 Deanna Cooper * d 0 0 0 0 1 0 0 0
17 Alex Franco * a 0 0 0 0 1 1 2 1
19 Marina Azab * g 0 0 0 0 1 0 2 1
21 Sarah Stephenson * m 0 0 0 0 1 0 2 0
23 Alexandra Lettre * d 0 0 0 0 9 1 5 4
24 Tashariff Carr 0 0 0 0 0 0 0 0
25 Carly Plaisance 0 0 0 0 3 0 2 0
Totals 5 1 11 7 32 6 30 14
19 Marina Azab (L, 0-7)	 12 32:47 5 17
25 Carly Plaisance 5 27:13 4 9
PIM: Kelsey Fairley 1-120
College of Mt. St. Vincent 2 0 2
Sage Colleges 5 4 9
College of Mt. St. Vincent 26 17 43
Sage Colleges 13 19 32
College of Mt. St. Vincent 6-9 6-8 12 -17
Sage Colleges 4-15 4-13 8 -28
College of Mt. St. Vincent 10 7 17
College of Mt. St. Vincent 2-4 1-2 3 -6
Sage Colleges 0-1 0-0 0 -1
Sage Colleges 5 6 11
Sage Colleges 8 12 20
Sage Colleges 19:55 Kelsey Fairley : - YELLOW CARD
Officials and game personnel: Colleen Belanger ; Melinda Petre ; Andrea Bourgeois ; Ann King


It's a bracelet made with 18K pink and white gold. This jewel is genuine Made in Italy.
Lenght: 18 cm (7.09 In). Balls Width: 0.3 cm (0.118 In). Weight: 1.7 gr (approx 0.06 oz).
The item "SOLID 18K ROSE & WHITE GOLD BRACELET WITH MINI FACETED BALLS 7.09 MADE IN ITALY" is in sale since Friday, October 25, 2013. This item is in the category "Jewelry & Watches\Fine Jewelry\Fine Bracelets\Precious Metal without Stones". The seller is "gioielleria-assodiori" and is located in Brescia. This item can be shipped worldwide.


text:
\section{Introduction}

It is most intriguing to observe that matter comes in different phases.
Usually, by a change of temperature one may switch between the different phases.
Close to zero temperature quantum fluctuations dominate over thermal fluctuations, and quantum systems  undergo  quantum phase transitions (QPTs) as a result of a change of an external  control parameter~\cite{sachdev:book}.

Discovery of new and exotic quantum phases and critical points, such as topologically ordered phases~\cite{wen:book}, quantum spin liquids~\cite{diep:book}, deconfined quantum critical points~\cite{Senthil05032004, PhysRevB.70.144407}, which are not encompassed by the Landau's theory of phase transitions, recently stirred significant interest into the study of QPTs.
Moreover, it was found that from quantum information theory perspective quantum phases and QPTs can be distinguished and characterized in terms of quantum entanglement~\cite{PhysRevA.66.032110, Osterloh2002}.
Entanglement measures are able to determine critical properties of the systems, in particular the positions of the critical points~\cite{RevModPhys.80.517}.

In the present paper we study how a specific entanglement quantifier, the \textit{bipartite entanglement per bond}~\cite{PhysRevA.81.032304}, can be used for a fast and computationally rather inexpensive determination of quantum critical points and other characteristic features of the phase structure for various one-, two- and three-dimensional quantum spin models.
This quantifier does not require the calculation of expectation values from the states but is obtained directly from the representation of a state. This is the reason why this quantifier comes at low numerical cost. Calculation of expectation values for two and three-dimensional systems is numerically expensive, that is why this quantifier is particularly useful for the analysis in 2D and 3D. The spin-1/2 3D XY model in a transverse field is studied systematically here for the first time.

The entanglement per bond is obtained directly from a tensor network representation of the ground state wave-function.
Tensor networks (TN)~\cite{1751-8121-42-50-504004, doi:10.1080/14789940801912366} provide a modern and promising tool for the numerical investigation of many-body systems.
The basic idea of TN methods is to represent the wave function of a many body quantum system by a network of interconnected tensors. For a recent review see~\cite{orus:review}.
For one-dimensional (1D) systems the best known tensor network states are  matrix product states (MPS)~\cite{doi:10.1080/14789940801912366}. Their direct generalization to 2D and 3D are the projected entangled pair states (PEPS)~\cite{Verstraete:arxiv0407066}. Details about MPS and PEPS can be found in~\cite{SCH10, PhysRevB.81.174411, PhysRevLett.101.090603, PhysRevB.87.085130}.

For our investigation we choose three spin-$1/2$ quantum models with nearest neighbor interactions and analyze them in the thermodynamic limit: the XY model (with quantum Ising model as a special case) and the XXZ model both in a transverse magnetic field. The models are investigated in one- (spin ring), two- (square lattice), and three (cubic lattice) dimensions.
We use the imaginary-time evolution for the determination of the ground states in the TN representation.
The entanglement per bond is calculated directly from the MPS and PEPS representation of the ground states.

The paper is organized as follows. In Sec.~\ref{bipart} we review the definition of the entanglement per bond and comment on its physical meaning. In Sec.~\ref{numerres} we present numerical results along with a detailed discussion. Conclusions are made in Sec.~\ref{conclu}.

\section{Bipartite entanglement per bond}\label{bipart}

In this section we define the bipartite entanglement  per bond $S_{\rm PB}$ in terms of the bond vectors
characterizing the TN. We comment on its physical interpretation and its ability to describe the entanglement properties of the state. Strictly speaking $S_{\rm PB}$ is not an experimentally measurable quantity, since it
depends on a specific representation of a quantum state as a TN.

Ground states in TN representation are obtained either  variationally or via imaginary-time evolution~\cite{CPA:CPA3160070404} based on a Trotter expansion~\cite{trotter} of the evolution operator.
In the present paper we use time-evolving block decimation (TEBD)~\cite{VID2007} to determine ground states of one-dimensional systems and the `simple update' scheme~\cite{PhysRevLett.101.090603} in 2D and 3D. The algorithms we use are well-known, so we do not provide details of their implementation.

The TEBD algorithm naturally leads to a ground state in the canonical form of MPS~\cite{vidal:3,PhysRevLett.93.040502,SCH10}. In this form, besides tensors $A$ at each site one also has  bond vectors $\vec{\lambda}$ at each bond of the tensor network. Within the given canonical MPS the bond states (bond vectors) can be regarded as renormalized bases of the physical degrees of freedom of the many body system (e.g. `effective' spins). Thus bond vectors can be treated as Schmidt coefficients in the wave function decomposition, i.e. they are objects which describe entanglement within the state. Moreover, the reduced density matrix of the state can be expressed approximately via virtual (bond) degrees of freedom, i.e. via the bond vectors. Unfortunately, no {\it exact}  canonical form for PEPS exists, but the `simple update'~\cite{PhysRevLett.101.090603,PhysRevB.86.195137} algorithm for imaginary-time evolution leads to a ground state in {\it approximate} canonical form of PEPS. Thus, bond vectors can be used to obtain the bipartite entanglement per bond in this case as well.

The numerical cost of the TEBD algorithm is $\mathcal{O}(m^3)$ with $m$ the bond dimension. The numerical costs for `simple update' procedure in 2D and 3D are $\mathcal{O}(m^9)$ and $\mathcal{O}(m^{15})$ respectively.
Notice, that the calculation of expectation values from a state given in MPS or PEPS representation requires numerically expensive (especially in 2D and 3D) tensor contraction procedure, but the bipartite entanglement per bond is obtained directly from the wave function tensor network representation, which makes this quantifier so attractive.

The bipartite entanglement per bond $S_{\rm PB}$ is directly defined in terms of the components of the bond vectors $\lambda_i$ which are normalized to satisfy  $\sum_i \lambda_i^2=1$.  Then, $S_{\rm PB}$ is defined as the entanglement entropy~\cite{nielsen:book} or von Neumann entropy
\begin{equation}
S_{\rm PB}= -\sum_i \lambda_i^2 \log_2 \lambda_i^2.
\end{equation}
In practice, we find that the bond vectors connecting to a given site $i$ are approximately equal, which is a consequence of the translational symmetry of the tensor network we implement.  As a consequence, we  average the bond vectors connecting to a site $i$ for the calculation of $S_{\rm PB}$.

Note that the  maximally possible value for $S_{\rm PB}$ (measuring the maximally possible entanglement in the state) is dependent on the  chosen bond dimension $m$ of the MPS or PEPS representation. This means that such a representation may not be able to accurately describe states close to critical points where entanglement may be very
large. Still, the calculated entanglement per bond provides at least semi-quantitative information on the phase structure of the many-body system.

\section{Numerical results and interpretation}\label{numerres}

The present section provides numerical results for the bipartite entanglement per bond  for the Ising, XY and XXZ models in a transverse field in one, two, and three dimensions. Ground states are obtained via imaginary-time evolution algorithms: time-evolving block decimation (TEBD) for modeling ground states of one-dimensional systems and the `simple update' scheme for two- and three-dimensional systems. We choose the spin ring for one-dimensional geometry, the square lattice in 2D and the cubic lattice in 3D always with periodic boundary conditions and translationally invariant. Critical points obtained from this measure dependence are compared to results from previous studies, based on other algorithms.

Imaginary-time steps are proceeded until the convergence of bond vectors is reached. As a check for a good ground state we use the condition of approximate equality of all bond vectors, that means presence of rotational symmetry in the ground state.
Time step size in the imaginary-time evolution is reduced repeatedly during convergence. For TEBD we use MPS bond size up to $m=40$. For the `simple update' algorithm we take bond sizes $m=4$ and $m=2$ in 2D and 3D, correspondingly.

\subsection{Anisotropic XY model}

We first study the anisotropic XY model in a transverse magnetic field,
\begin{equation}
 H^{\rm XY}=-\sum_{\langle i,j\rangle} \left\{ (1+\gamma)  S_i^x   \otimes S_{j}^x + (1-\gamma)  S_i^y   \otimes S_{j}^y \right\}
 +h\sum_i S_i^z,
\end{equation}
where $\langle i,j\rangle$ indicates a summation over nearest neighbors. It includes the Ising model as a special case ($\gamma=1$). We use periodic boundary conditions, and
the spin operators  $S^{\alpha}=\frac{1}{2} \sigma^{\alpha}$ are related to the Pauli matrices $\sigma^{\alpha}$.
The model has two parameters, the anisotropy  $\gamma$ and the magnetic field $h$.

The one-dimensional XY model can be solved analytically~\cite{LIE61,sachdev:book,henkel:book}), and as guide for the reader its well-known phase diagram is shown schematically in Figure~\ref{xy1ddiagram}.  There are ferromagnetic and paramagnetic phases which are separated by the black dashed critical lines. On the red circle $h^2+\gamma^2=1$ the model is classical, where we expect entanglement to vanish. It is known that  correlation functions have an oscillatory tail~\cite{PhysRevA.2.1075}
inside this circle. Consequently, this region often is called `oscillatory'. The line $\gamma=0$ separates  two different ferromagnetic phases: the $x$-phase (upper half plain) and the $y$-phase (lower half plain).

The phase structure of the XY model in 2D is similar to the one shown for 1D~\cite{0305-4470-17-14-013, PhysRevA.81.032304}. It is classical for
$(h/2)^2+\gamma^2=1$.
For more details on the phase diagram of 1D and 2D anisotropic XY models see~\cite{1751-8121-43-50-505302,0305-4470-17-14-013}.
\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{1dxydiagram.eps}
    \caption{\footnotesize
    Phase diagram of the 1D XY model. Black dashed lines indicate phase separation lines. Green dashed lines $\gamma=1$, $\gamma=0.7$, $\gamma=0.5$ and $h=0.5$ indicate the cases presented in Figs.~\ref{SPB1D2D3D-ising},~\ref{SPB1D2D3D-xy07},~\ref{SPB1D2D3D-xy05}, and~\ref{SPB1D2D3D-xyh1}. The dots mark points where $S_{\rm PB}$ shows special characteristics. (PM: Paramagnetic phase, FM: Ferromagnetic phase).
    }\label{xy1ddiagram}
\end{figure}

The 3D spin-$1/2$ anisotropic XY model in a transverse field has not yet been studied in detail according to our knowledge. Our results suggest that the 3D XY model has a similar phase structure  as its 1D and 2D counterparts, and that it is classical on the circle $(h/3)^2+\gamma^2=1$. However, the bipartite entanglement per bond does not provide enough information to determine the detailed characteristics of the phases. In order to do so, one has  to calculate expectation values of various observables. The entanglement per bond $S_{\rm PB}$ just provides information about the position of critical points as well as lines of vanishing entanglement (`classical' lines).

We now discuss results for $S_{\rm PB}$ along various lines in the phase diagram (indicated as green dashed
in Fig.~\ref{xy1ddiagram}): $\gamma=1$ (Ising model), $\gamma=0.7$ and $\gamma=0.5$ as well as $h=0.5$.

The results for $\gamma=1$ are shown in Figure~\ref{SPB1D2D3D-ising}.
In 1D our TEBD calculations provide a critical point in very good agreement with the analytical result: $h_{\rm{c}}^{\rm 1D} \approx 1.00$.
The 2D quantum Ising model cannot be solved analytically, and various methods are applied to solve it numerically,
e.g. quantum Monte-Carlo (QMC) methods.
Such calculations find a transition between a ferromagnetic and a paramagnetic phase at a critical point $h_{\rm c}^{\rm 2D}=3.044$~\cite{PhysRevE.66.066110}.
The tensor network implementation applied here produces numerical results significantly faster than QMC calculations,
however, with less precision: it determines a critical point at $h_{\rm{c}}^{\rm 2D} \approx 3.26$. More precise results can be obtained with more elaborate tensor network implementations and larger bond sizes~\cite{orus:review}. However, it is our goal to investigate $S_{\rm PB}$ properties using small numerical cost, i.e. with small virtual bond dimension.

The 3D quantum Ising model cannot be solved analytically as well. The series expansion study in the $T \rightarrow 0$ limit~\cite{0305-4470-27-16-010} predicted the critical point of $h_{\rm{c}}^{\rm 3D} \approx 5.14$. Another study based on `simple update' scheme was performed in~\cite{PhysRevB.87.085130} and the critical point was determined at $h_{\rm{c}}^{\rm 3D} \approx 5.29$ from  the ground state magnetization. The magnetization calculations presented in~\cite{PhysRevB.87.085130} require calculation of expectation values, that is the tensor network contraction procedure. We obtain a result ($h_{\rm{c}}^{\rm 3D} \approx 5.30$) in good agreement with latter one, but without the need to calculate a matrix element
explicitly.

\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{123ising.eps}
    \caption{\footnotesize
    Bipartite entanglement per bond for $\gamma=1$ (Ising model) in 1D (chain), 2D (square lattice), 3D (cubic lattice) as a function of the magnetic field $h$.
    2D and 3D results are multiplied by a factor of 10 and 15, respectively.
    Bond dimensions: $m^{\rm 1D}=20$, $m^{\rm 2D}=4$, $m^{\rm 3D}=2$.
    }\label{SPB1D2D3D-ising}
\end{figure}

Numerical results for $\gamma=0.7$ and $\gamma=0.5$ are shown in the Figures~\ref{SPB1D2D3D-xy07} and~\ref{SPB1D2D3D-xy05}, respectively. $S_{\rm PB}$ has two characteristic features: at the ferromagnetic-to-paramagnetic phase transition  it shows a maximum, and  it is zero at the boundary of the oscillatory region $(h/d)^2+\gamma^2=1$ ($d=1,2,3$). Both points are easily identified in the figures.

In the case $\gamma=0.7$ (Figure~\ref{SPB1D2D3D-xy07}) characteristic features are seen at $h_o^{\rm 1D} \approx 0.71$ and at $h_c^{\rm 1D} \approx 1.00$ for 1D. These results perfectly agree with  theoretical predictions~\cite{PhysRevA.81.032304,1751-8121-43-50-505302}. The 2D result $h_o^{\rm 2D} \approx 1.42$ perfectly agrees with the prediction from $(h/d)^2+\gamma^2=1$, while $h_c^{\rm 2D} \approx 2.89$ differs slightly  from the reference value $h_c^{\rm 2D}=2.72$ obtained from finite size scaling~\cite{0305-4470-17-14-013}. The 3D boundary point $h_o^{\rm 3D} \approx 2.14$  satisfies  $(h/3)^2+\gamma^2=1$, and we obtain the 3D ferromagnetic-to-paramagnetic critical point at $h_c^{\rm 3D} \approx 4.63$.

\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{123xygamma07.eps}
    \caption{\footnotesize
    Bipartite entanglement per bond for $\gamma=0.7$ in 1D (chain), 2D (square lattice), 3D (cubic lattice)
    as a function of magnetic field $h$.
    2D and 3D results are multiplied by a factor of 12 and 24, respectively.
    Bond dimensions: $m^{\rm 1D}=20$, $m^{\rm 2D}=4$, $m^{\rm 3D}=2$.
    }\label{SPB1D2D3D-xy07}
\end{figure}

For $\gamma=0.5$  we obtain in 1D $h_o^{\rm 1D} \approx 0.87$ and $h_c^{\rm 1D} \approx 1.00$ again in perfect agreement with theoretical predictions. Our 2D result $h_o^{\rm 2D} \approx 1.73$  agrees with the theory while $h_c^{\rm 2D} \approx 2.64$ differs slightly (the reference value is $h_c=2.5$~\cite{0305-4470-17-14-013}).  We observe zero entanglement at $h_o^{\rm 3D} \approx 2.60$, which satisfies the expression $(h/3)^2+\gamma^2=1$. The 3D ferromagnetic-to-paramagnetic critical point for $\gamma=0.5$ is determined to be at $h_c^{\rm 3D} \approx 4.17$.

\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{123xygamma05.eps}
    \caption{\footnotesize
    Bipartite entanglement per bond for $\gamma=0.5$ in 1D (chain), 2D (square lattice), 3D (cubic lattice)
    as a function of magnetic field $h$.
    2D and 3D results are multiplied by a factor of 12 and 24, respectively.
    Bond dimensions: $m^{\rm 1D}=20$, $m^{\rm 2D}=4$, $m^{\rm 3D}=2$.
    }\label{SPB1D2D3D-xy05}
\end{figure}

Figure~\ref{SPB1D2D3D-xyh1} represents bipartite entanglement per bond for the XY model in all three dimensions as a function of anisotropy parameter $\gamma$ at fixed magnetic field $h=0.5$.
The entanglement measure peaks at $\gamma=0$ indicating the phase transition between two different ferromagnetic phases and vanishes at points which correspond the equation $(h/d)^2+\gamma_o^2=1$.
Figure~\ref{SPB1D2D3D-xyh1small} displays an enlarged view of the region  where entanglement vanishes for positive $\gamma$.
The obtained values for $\gamma^{\rm 1D}\simeq \pm 0.866$, $\gamma^{\rm 2D}\simeq \pm 0.968$, $\gamma^{\rm 3D}\simeq \pm 0.986$ agree to a high precision with the expected theoretical values.

\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{123xyh1.eps}
    \caption{\footnotesize
    Bipartite entanglement per bond for $h=0.5$ in 1D (chain), 2D (square lattice), 3D (cubic lattice)
    as a function of anisotropy parameter $\gamma$.
    2D and 3D results are multiplied by a factors 18 and 30, respectively.
    Bond dimensions: $m^{\rm 1D}=40$, $m^{\rm 2D}=4$, $m^{\rm 3D}=2$.
    }\label{SPB1D2D3D-xyh1}
\end{figure}

\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{123xyh1small.eps}
    \caption{\footnotesize
   Bipartite entanglement per bond for h=0.5 in 1D (chain), 2D (square lattice), 3D (cubic lattice)
    as a function of anisotropy parameter $\gamma$.  Displayed region shows those positive values of $\gamma$, where entanglement vanishes.
    1D, 2D and 3D results are multiplied by a factors 15, 200, and 400, respectively.
    Bond dimensions: $m^{\rm 1D}=40$, $m^{\rm 2D}=4$, $m^{\rm 3D}=2$.
    }\label{SPB1D2D3D-xyh1small}
\end{figure}

The boundary points of the oscillatory region are obtained numerically up to a very high precision as predicted by the relation $(h/d)^2+\gamma^2=1$. This observation nicely underlines that MPS and PEPS tensor network states are particularly able to model ground states with a low amount of entanglement, that is to model states for which a low bond dimension is enough.

On the other hand, our results for the phase boundaries which are  characterized by a maximum value of $S_{\rm PB}$ differ from the theoretical predictions in 2D presented in Ref.~\cite{0305-4470-17-14-013}.
This is due to the low virtual bond dimension of the PEPS used here, i.e., its impossibility to capture the large amount of entanglement needed to determine the critical point more precisely. Consequently, we would expect that the results for the 3D phase boundaries are even less precise than our 2D results.

From the Figures shown above in this section we conclude that $S_{\rm PB}$ is quite capable of determining important features of the phase diagram for a wide range  of model parameters at relatively small numerical cost. The results for the ferromagnetic-to-paramagnetic phase transition in the 3D XY model, namely $h_c^{\rm 3D} \approx 4.17$ for $\gamma=0.5$ and $h_c^{\rm 3D} \approx 4.63$ for $\gamma=0.7$, were not obtained before to the best of our knowledge.

\subsection{XXZ model}

Next we study the spin-$\frac{1}{2}$ XXZ (anisotropic Heisenberg) model in a transverse magnetic field,
\begin{equation}\label{Ising Hamiltonian}
H^{\rm XXZ}=\sum_{\langle i,j \rangle} \left\{ S_i^x \otimes S_j^x + S_i^y \otimes S_j^y + \Delta \, S_i^z \otimes S_j^z \right\}-\sum_i h \, S_i^z
\end{equation}
as a function of the anisotropy parameter $\Delta$ and the magnetic field $h$.

The phase structure of the XXZ model was studied extensively in 1D~\cite{PhysRev.150.321, PhysRev.150.327,PhysRev.151.258,PhysRevA.85.052128,  PhysRevB.49.9702, Mikeska01}, 2D~\cite{PhysRevA.85.052128,PhysRevB.65.092402,PhysRevB.64.214411}, and 3D~\cite{PhysRevB.65.092402}.
In all three dimensions the model shows three phases~\cite{PhysRevB.65.092402}: an antiferromagnetic (N\'eel) phase, a XY (spin-flopping) phase and a ferromagnetic  phase. These three phases are separated by two critical lines, and we denote them as $h_c$ and $h_s$.
For 1D the well-known phase diagram can be obtained analytically using the Bethe Ansatz ~\cite{PhysRev.150.321,PhysRev.150.327,PhysRev.151.258}, and it is shown in Figure~\ref{xxz1ddiagram}.
The ferromagnetic phase is separated from spin-flopping phase by the line $h_s=d \, (1+\Delta)$ ($d=1,2,3$ is the dimension of the model)~\cite{PhysRev.135.A640,0953-8984-11-24-311,PhysRevB.65.092402}. In 1D the N\'eel phase is separated from the spin-flopping phase by the curve $h_c$~\cite{PhysRev.151.258,Cloizeaux1966}
\begin{equation}
h_c=
  \frac{\pi \sinh \lambda}{\lambda}\sum_{n=-\infty}^{\infty} {\rm sech} \frac{\pi^2}{2\lambda}(1+2n)
\end{equation}
with  $\lambda= {\rm arccosh} \Delta$.
In particular, at zero magnetic field the ferromagnetic-to-XY critical point is at $\Delta=-1$ and the XY-to-antiferromagnetic critical point at $\Delta=1$.

Similar phase diagrams for the two- and three-dimensional XXZ models, based on quantum Monte Carlo studies, can be found in~\cite{PhysRevB.65.092402}. The most notable difference
to the 1D phase diagram shown here is the fact that the critical lines $h_c$  have a finite derivative with respect to $h$ at $\Delta=1$.

\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{1dxxzdiagram.eps}
    \caption{\footnotesize
    Phase diagram of the 1D XXZ model. The line $h_s$ separates the XY phase from the ferromagnetic phase (FM). The curve $h_c$ separates the anti-ferromagnetic (AFM) from the XY phase. The green dashed lines $h=1$ and $\Delta=1.5$ correspond to the cases discussed in detail in the text and in Figures~\ref{SPB1D2D3D-xxz-h1} and \ref{SPB1D2D3D-xxz-delta15}. The black dots indicate the critical points obtained from the entanglement per bond.}\label{xxz1ddiagram}
\end{figure}

For our numerical studies we choose three cases: $h=0$ (Figure~\ref{SPB1D2D3D-xxz}) and $h=1$  (Figure~\ref{SPB1D2D3D-xxz-h1}) as well as $\Delta=1.5$  (Figure~\ref{SPB1D2D3D-xxz-delta15}). These lines are denoted as green dashed lines in the phase diagram \ref{xxz1ddiagram}.

Figure~\ref{SPB1D2D3D-xxz} presents our results for the bipartite entanglement per bond at zero magnetic field as a function of $\Delta$. From the figure we see that critical points $\Delta=\pm 1$ are obtained correctly. Notice that the critical point $\Delta=1$ is characterized by a maximum of the entanglement, but that at the critical point $\Delta=-1$ the entanglement vanishes. Moreover we observe that at $\Delta=-1$ $S_{\rm PB}$ shows a discontinuity in 1D, while it increases slowly in 2D and 3D.

\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{123xxzh0.eps}
    \caption{\footnotesize
    Bipartite entanglement per bond for the XXZ model with zero magnetic field in 1D (chain), 2D (square lattice), 3D (cubic lattice)
    as a function of anisotropy parameter $\Delta$.
    2D and 3D results are multiplied a factor of 5 and 6, respectively.
    Bond dimensions: $m^{\rm 1D}=20$, $m^{\rm 2D}=4$, $m^{\rm 3D}=2$.
    }\label{SPB1D2D3D-xxz}
\end{figure}

Figure~\ref{SPB1D2D3D-xxz-h1} shows our results for the bipartite entanglement per bond as a function of $\Delta$ at $h=1$. The 1D critical points are in a very good agreement with exact values~\cite{PhysRev.150.327,PhysRev.151.258}: the ferromagnetic to spin-flopping phase transition occurs at $\Delta_s^{\rm 1D}=0$ and the spin-flopping to antiferromagnetic transition at $\Delta_c^{\rm 1D}=2.75$. The 2D critical points are found at $\Delta_s^{\rm 2D}=-0.5$ and $\Delta_c^{\rm 2D}=1.18$, and the 3D critical points at $\Delta_s^{\rm 3D}=-0.67$ and $\Delta_c^{\rm 3D}=1.07$. The values obtained for $\Delta_s$ in all three dimensions correspond to the relation $h_s=d \, (1+\Delta)$ with dimensions $d=1,2,3$. Our values obtained for $\Delta_c$ for the two- and three-dimensional XXZ model are in a good agreement with quantum Monte Carlo results given in~\cite{PhysRevB.65.092402}.

\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{123xxzh1.eps}
    \caption{\footnotesize
    Bipartite entanglement per bond for XXZ model with $h=1$ in 1D (chain), 2D (square lattice), 3D (cubic lattice) geometries
    as a function of anisotropy parameter $\Delta$.
    2D and 3D results are multiplied a factor of 8 and 12, respectively.
    Bond dimensions: $m^{\rm 1D}=20$, $m^{\rm 2D}=4$, $m^{\rm 3D}=2$.
    }\label{SPB1D2D3D-xxz-h1}
\end{figure}

Figure~\ref{SPB1D2D3D-xxz-delta15} shows results for $S_{\rm PB}$ as a function of the magnetic field $h$ at  $\Delta=1.5$.
The XXZ model at $\Delta=1.5$ was studied analytically in 1D~\cite{PhysRev.150.327,PhysRev.151.258} and was investigated numerically in 2D and 3D~\cite{PhysRevA.81.032304,PhysRevB.65.092402}. These studies predict two critical points for each dimensionality. From equation $h_s=d \, (1+\Delta)$ one obtains $h_s^{\rm 1D}= 2.5$, $h_s^{\rm 2D}= 5.0$, $h_s^{\rm 3D}= 7.5$, and our results agree with these values. For the one-dimensional model the exact solution gives $h_c^{\rm 1D} \simeq 0.0866$~(\cite{PhysRev.150.327}), and our result $h_c^{\rm 1D} \simeq 0.09$ is very close. Our 2D and 3D results are $h_c^{\rm 2D} \approx 1.8$ and $h_c^{\rm 3D}\approx 3.2$ are in a good agreement with previous quantum Monte Carlo studies~\cite{PhysRevB.65.092402}.

From  Figures~\ref{SPB1D2D3D-xxz},~\ref{SPB1D2D3D-xxz-h1}, and~\ref{SPB1D2D3D-xxz-delta15} we conclude that $S_{\rm PB}$ is capable of providing quite some insight into the phase structure of a quantum spin model. One not only obtains critical points, but also points or lines where the system behaves classically. The variation of $S_{\rm PB}$ in between such lines provides insight how the entanglement of the various ground states changes as a function of the control parameters.
Of course, for a more detailed investigation one then would need to calculate relevant expectation values in order to obtain physical properties in interesting regions. The identification of such regions is easily guided
by the $S_{\rm PB}$, which is obtained at a rather low numerical cost.
\begin{figure}[h!]
\centering
    \includegraphics[width=0.6\textwidth]{123xxzDelta15.eps}
    \caption{\footnotesize
    Bipartite entanglement per bond for the XXZ model at $\Delta=1.5$ in 1D (chain), 2D (square lattice), 3D (cubic lattice)
    as a function of external magnetic field $h$.
    2D and 3D results are multiplied by factors 7 and 12, respectively.
    Bond dimensions: $m^{\rm 1D}=20$, $m^{\rm 2D}=4$, $m^{\rm 3D}=2$.
    }\label{SPB1D2D3D-xxz-delta15}
\end{figure}

From Figures~\ref{SPB1D2D3D-xxz},~\ref{SPB1D2D3D-xxz-h1}, and~\ref{SPB1D2D3D-xxz-delta15} we observe interesting differences for $S_{\rm PB}$ at the critical points in different spatial dimensions. E.g., at the transition from the ferromagnetic to the spin-flopping phase $S_{\rm PB}$ shows a jump in 1D, for 2D and 3D it shows a cusp. The numerical results indicate that the entanglement structure of the ground state of the XXZ model in different spatial dimensions differs not only quantitatively but also qualitatively. Understanding the reasons for these differences requires further analysis which is beyond the bipartite entanglement per bond quantifier.

\section{Conclusions}\label{conclu}

In the present paper the bipartite entanglement per bond  $S_{\rm PB}$ was calculated for the Ising, anisotropic XY and XXZ models in a transverse magnetic field and in one, two, and three dimensions for various sets of control parameters.
All obtained results are in very good agreement with previous studies. They show that bipartite entanglement per bond is an efficient, easy-to-calculate and relatively precise tool for the determination of the some characteristics  of the phase diagram of quantum models.
It conveniently uses the tensor network representation of a state.

The three-dimensional anisotropic XY model with transverse field on a cubic lattice was studied numerically for the first time. The obtained boundary points of the oscillatory region satisfy the relation $(h_o/3)^2+\gamma^2=1$.

We observe that the bipartite entanglement per bond determines  characteristic features of the phase diagram better if states with a low amount of entanglement are involved. For our 2D and 3D calculations we took rather low virtual bond sizes and therefore our PEPS can only model states with rather low entanglement. Moreover, if more detailed
questions about the phase diagram need to be answered for specific regions (e.g. the magnitude of the magnetization), then calculations of matrix elements cannot be avoided.

The present paper was geared towards a semi-quantitative analysis of the bipartite entanglement per bond. An interesting and promising task is the quantitative investigation which requires implementation of the symmetries of the ground states into the imaginary-time evolution algorithms. That would enable higher virtual bond dimensions for MPS and PEPS and the calculation of the entanglement spectrum of the state.

Besides the  geometries studied in the present paper (spin ring, square lattice, cubic lattice), the bipartite entanglement can also be used to characterize properties of  quantum models on hyperbolic lattices~\cite{PhysRevE.86.021105}, after modification of the `simple update' algorithm for the ground-state calculation. Moreover, the present study should be extended to spin-1 systems.

{\small
\bibliographystyle{unsrtNoTitles}

redpajama_set_name: RedPajamaArXiv


text:
Piotr Sarzyński (ur. 4 czerwca 1955) – polski dziennikarz i publicysta, zajmujący się problematyką kulturalną w tygodniku "Polityka". Krytyk sztuki, autor książek popularyzujących sztukę. Z wykształcenia socjolog.

Życiorys
Pracował jako asystent na Wydziale Socjologii UW, nauczyciel w wiejskiej szkole w Wetlinie w Bieszczadach. Był też urzędnikiem. Jako dziennikarz początkowo pracował w "Radarze" (od 1985). Od 1986 do chwili obecnej pisze artykuły o tematyce kulturalnej dla tygodnika "Polityka", z którym jest ściśle związany.

W latach 1988-1996 współautor i prowadzący liczne programy w TVP (m.in. "Studio Otwarte", "Kawa czy herbata?", "Zapis", "Stoper"). Współprowadzący programu "Sztuka życia" w Polsat Café.

Publikacje
 Przewodnik po rynku malarstwa (1999)
 Kronika śmierci przedwczesnych (2000, wspólnie z Mają Wolny)
 Leksykon samobójców (2002)
 Wrzask w przestrzeni. Dlaczego w Polsce jest tak brzydko? (2012)

Nagrody
 Medal im. Krzysztofa Komedy
 Nagroda Artystyczna Hestii
 medal Gloria Artis

Życie prywatne
Żonaty, ma troje dzieci: Igora (ur. 1986), Idalię (ur. 1998) i Julię (ur. 2000).

Przypisy

Linki zewnętrzne
Artykuły Piotra Sarzyńskiego w "Polityce"

Polscy dziennikarze kulturalni
Polscy krytycy sztuki
Polscy publicyści
Urodzeni w 1955


text:
Nitya Ramanan | Sep 2, 2005
As I was waiting for a friend one weekend at the India Community Center, Sunnyvale, I got into a conversation with a parent who was waiting for her daughter attending Hindi class. Upon learning that I work at India Currents, she immediately told me how much she enjoyed reading the magazine, what an immense resource it is for her, and how it had (indirectly) helped her land a job of her choice. As she reeled out titles of many articles that she had enjoyed reading in the past months, I couldn't help but feel a sense of accomplishment and pride.
When people learn of my association with India Currents, their reaction hasn't always been this exuberant. Sometimes I have been met with a blank look, indicating their unfamiliarity with the magazine. Occasionally people say, "Oh yes, I know that magazine. Don't you guys have many listings of local Indian businesses?"
India Currents started in 1987 when the Indian-American population wasn't as sizeable as it is today. Focusing on the immediate needs of the community, the magazine informed readers of Indian arts and cultural events, and Indian business establishments in the area.
Over the years, as the desi population has burgeoned, cultural tastes have also diversified. As our immigrant community comes of age, we no longer feel threatened by the cultures of our adopted home. Instead, we try to instill in our children values from both countries.
The magazine's content has also evolved to include not only Karnatik and Hindustani music, and classical dances from India, but also a fusion of modern and traditional, East and West. Today India Currents reflects the state and perspectives of an eclectic readership. Our Youth column gives voice to a younger generation that walks a tightrope between liberal and traditional cultural values. In the Forum column we debate important issues affecting India and the United States. Our Recipes column encompasses even the most mundane of vegetables like the rutabaga in the flavors of the desi kitchen.
Readers no longer pick up a magazine exclusively to learn of the whereabouts of the nearest grocery store. Instead, they look for information that will bring an awareness into their changing lives as Indian Americans. We at India Currents have been working hard to reflect the voices of our community. But to succeed in that task, we need to hear from you too. Write to us and tell us what you would like to see in our pages. It is this two-way exchange of thoughts that fosters insightful content in the pages of the magazine.


Supreme is now incredibly popular in street wear and fashion, with pieces selling often "reselling"for multiple times its original price. Its just crazy with 11 stores ( six which are located in japan) and with its online shop, Supreme takes in the amount of about 1 billion dollar brand. Louis Vuitton made a collab with supreme and this shirt originally was 150$ and now in today's markets its worth about 700-1200$ just for a shirt. Supreme overall is one of the best brands of today and are doing really good in today's markets. Michael Kors sold a stake of their company to supreme and their company increased by 25% in all accessories. Supreme is just big these days and will be collaborating with even bigger companies.


Could not stop praising the Oberoi Mall for one unique aspect – Free WiFi. Dunno how many people know and use it. However, I have used it and its pretty decent. Basic photo ID required.
Oberoi Mall is awesome… I used to stay 10 mins walking distance from there once upon a time. Retail therapy in Bangalore (where I stay now) doesn't feel the same..
@Jagadeesh: Hey, thanks for that tip! I didn't know it either. Will definitely avail of it the next time I go…preferably on a weekday, considering the hordes that throng there on weekends.
@Tamanna: Awww, what are you saying? Bangalore embraced the organized retail culture much before Mumbai did. What of all those places on Brigade Road? I don't think I ever saw them as busted to the seams as the average mall in Mumbai is.


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Only our registered users can earn bonus points, participate in a raffle and book or purchase a tour.
How do I take part in a raffle?
In order to participate, you must pay the minimum $10 contribution towards a lot's fund. Earning bonus points that will increase your chances to win is voluntary.
How many contributions can I make per lot?
For each lot, you can make only one personal contribution allowing you to take part in the raffle and an unlimited number of sponsor contributions, each increasing your rating by 10 points.
What is a personal contribution?
A personal contribution is a fixed amount paid towards the price of a lot, increasing the contributor's rating by 10 points and allowing them to participate in a raffle.
In order to have a personal contribution debited from their account, a participant must post information about the relevant lot on a social network.
Deleting the post later will mean waiving one's right to participate in the raffle.
What is a sponsor contribution?
A sponsor contribution is a fixed amount paid towards the price of a lot and increasing the contributor's rating by 10 points.
A sponsor contribution can be made any number of times until the lot's fund is full.
What is a gift contribution?
A gift contribution can be made for another participant who has not yet made their personal contribution towards a chosen lot. The recipient will be informed of who sent the gift.
Rating points will be credited to the recipient's account.
How do you select a winner?
Once the lot's fund is full, 10 minutes after the last contribution the system will select a winner, that is, the participant with the highest rating. The winner will be offered to make use of the lot.
All participants will be informed of the raffle winner, their rating and the time when their personal contribution was paid. They will also be informed about the next three participants eligible for a win should the current winner waive their right to make use of the lot.
The winner will have 24 hours to confirm their profile details and the right to use the lot and 3 days to discuss their vacation dates with the tour organizer, as per the Terms and Conditions of our Public Tender Offer. Should the winner fail to confirm the above details with the website administration within allocated time, the system will select another winner.
Should more than one participants have the same winning number of points, the system will select the participant who made their personal contribution earlier than the others.
Once the winner has confirmed their right to use the lot, their rating will be reset to zero. Other participants' ratings will remain unchanged and will be eligible for other raffles.
Should the winner ignore their win and fail to confirm their right to use the lot, they will be excluded from the raffle and their rating points will remain unchanged and eligible for other raffles. The raffle will go ahead and the system will select another winner.
How do I find out who won?
All participants will be automatically notified of the relevant raffle's results, and a copy of the notification will be sent to their email provided in their dashboard.
The personal details listed in each participant's dashboard must be genuine, otherwise, should a participant win, they may be stripped of the right to make use of the lot.
Can the winner be denied the right to use the lot?
Yes, they can if an unmanageable language barrier occurs between the winner and the tour organizer or the winner fails to verify their details or confirm their intention to make use of the lot within allocated time.
Will I get my money back if the lot fails to raise enough money by the end of the raffle?
Yes. The lot's status will be changed to "unsuccessful" and the contributions collected will be automatically returned to participants' personal accounts.
How and in which circumstances do you refund users?
• The deadline for raising money for a lot or a crowdfunding project has passed. The money contributed by participants will be fully refunded to their personal accounts.
• The organizer cancelled a lot or a crowdfunding project before the fund was full. The money contributed by raffle participants / project sponsors will be fully refunded to their personal accounts.
• An unmanageable language barrier has occurred between the traveler and the tour organizer. A refund will be issued to the traveler's personal account as per the Terms and Conditions of our Public Tender Offer.
Please refer to our Public Tender Offer for more details. Or get in touch and we'll be happy to answer your questions.


Re: Auto update mass on drawings?
What I do is before creating the drawing I do the path you described.
Anytime you change the model - mass, you have to update the 3D model first, then the mass on the dwg will update automatically.
Have you got this box ticked?
MP5 for Solid Edge 2019 is now available for downloading and should address the property text update issue.