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News - reactions to
Fear inflation
Coronavirus characteristics
How the MEAN psychologists got us to comply with coronavirus restrictions
The British public's widespread compliance with the Government's draconian diktats has arguably been the most remarkable aspect of the coronavirus crisis. The unprecedented restrictions on our basic freedoms – in the form of lockdowns, travel bans and mandatory mask wearing – have been passively accepted by the large majority of people. Despite the lack of evidence for effectiveness of these extreme measures, and the growing recognition of their negative consequences, it seems most of us continue to submit to the ongoing restrictions on our lives. Why have we witnessed such capitulation?
A major contributor to the mass obedience of the British people is likely to have been the activities of government-employed psychologists working as part of the 'Behavioural Insights Team' (BIT). After outlining the structure and stated remit of the BIT, I will describe the strategies deployed by this group of psychological specialists to shape our behaviours in line with the Government's public health approach to coronavirus. In particular, I will highlight the four main tactics used in their COVID-19 communication campaigns to 'nudge' us towards compliance: a focus on the MESSENGER, EGO, AFFECT and NORMS (or 'MEAN' as an acronym), providing specific examples to illustrate how these influencers were put to work so as to get us to obey the Government's directives. Finally, the questionable ethics of resorting to these psychological interventions to promote compliance with an increasingly contested public health policy will be addressed.
The Behavioural Insights Team – structure and remit
The BIT was conceived in the Prime Minister's Office in 2010 as 'the world's first government institution dedicated to the application of behavioural science to policy' (Hallsworth et al., 2018). It is collectively owned by the UK Government, Nesta (a charity that views itself as an 'innovation foundation' and a 'champion of radical thinking'), and BIT's own employees. According to the BIT website, their team has rapidly expanded from a seven person unit working with the UK government to a 'social purpose company' operating in many countries around the world.
The stated aims of the BIT sound ambitious and altruistic. By working with a range of stakeholders (for example, governments and local authorities) the team aspire 'to improve people's lives and communities' by applying 'behavioural insights to inform policy, improve public services and deliver results for citizens and society'. Few would dispute that these sound like worthy goals. However, a closer inspection of the BIT's methods raises concerns about the moral integrity of applying them for the purpose of achieving of the Government's public health aims in regards to the coronavirus crisis.
A comprehensive account of the psychological approaches deployed by the BIT is provided in the document MINDSPACE: Influencing behaviour through public policy (Dolan et al., 2010). This report – produced by the Institute of Government – states that the application of behavioural strategies can achieve 'low cost, low pain ways of "nudging" citizens … … into new ways of acting by going with the grain of how we think and act' (p7) (My emphasis). By expressing the process of change in this way, this statement reveals a key difference between the BIT interventions and traditional government efforts to shape our behaviour: their reliance on tools that often impact on us subconsciously, below our awareness.
Historically, in addition to compulsion (via legislation and regulation), governments have used information provision and rational argument in their efforts to alter the behaviour of their citizens. Armed with the appropriate evidence about an issue – for example, the environmental cost of excess plastic – the expectation is that people rationally (and consciously) weigh up the pros and cons of each of their options and consider changing their behaviour accordingly. By contrast, many of the nudges delivered by the BIT are – to various degrees – acting upon us automatically, below the level of conscious thought and reason.
Before describing the specific BIT strategies deployed to maximise our compliance with the coronavirus restrictions, it is important to emphasise that these interventions are, for the most part, underpinned by a robust evidence base drawn from the psychological sciences. As such, these are powerful tools that should always be used responsibly.
The specific nudges used by the BIT
The BIT rely on a range of interventions to mould our activities so as to better align with Government policy. The specific strategies employed for this purpose can be summarised by the acronym MINDSPACE (as shown below).
We are influenced by the source of the information
We employ predictable shortcuts such as strongly avoiding losses
We are strongly influenced by what others do
We 'go with the flow' of pre-set options
Our attention is drawn to what is novel & seems personally relevant
Our acts are often influenced by subconscious cues
Our emotions powerfully shape our actions
We seek to be consistent with our public promises
We act in ways that make us feel better about ourselves
The four most relevant nudges deployed to gain the public's compliance with the coronavirus restrictions appear to be 'messenger', 'ego', 'affect' and 'norms' (or MEAN as a mnemonic), and specific examples of each of these strategies in action will be given below. Although described separately, these nudges often overlap and act together. Apart from MEAN, other tools from the MINDSPACE acronym have also, to some extent, been evident in the coronavirus campaign – one obvious example, the 'incentive' to avoid losses underpins the imposition of fines for breaking the 'rule of six' and the mandatory masks diktats.
The characteristics of the person communicating the message will significantly influence the degree to which the recipients take heed of the information conveyed. If the messengers are perceived as possessing high levels of authority, or to be worthy of admiration, people will be more likely to believe them and follow their advice and directives. Consequently, we've repeatedly witnessed the senior academic duo of Professor Chris Whitty and Sir Patrick Vallance (Chief Medical Officer and Chief Scientific Advisor, respectively) inform us of the latest COVID-19 statistics and projections, notably just before the Government is about to impose further restrictions on our freedoms. Similarly – playing on the widespread respect for NHS staff – nurses in full uniform continually appear on our TV screens bombarding us with the latest Government mantras.
The Government's behavioural specialists also recognise that messages delivered by people with whom we can identify are likely to be impactful. Hence, it is not incidental that the multiple voices on TV and radio urging us to wears masks, socially distance, or download the Government's track-and-trace app speak with a range of regional accents; to date I've heard Geordie, North West, West Midlands, South Western and Welsh, but I suspect this is not an exhaustive list. Similarly, the media messengers have included men and women, young and old, drawn from a variety of ethnic and socio-economic groups.
We all strive to maintain a positive view of ourselves and, in so doing, exhibit cognitive biases in the way we make sense of the world. For example, to preserve a virtuous self-image, each of us routinely display what psychologists refer to as a 'fundamental attribution error', whereby we take the credit for good outcomes while blaming others for bad ones. This inherent drive to protect our ego, to act and think in ways that make us feel better about ourselves, has been comprehensively exploited by the BIT specialists to nudge – nay, push – us to conform with coronavirus restrictions.
Aided by a mainstream media slavishly committed to promoting the Government's coronavirus narrative, throughout the crisis we have been bombarded with slogans and mantras that insist that compliance is akin to the altruism of helping others:
'STAY HOME, PROTECT THE NHS, SAVE LIVES'
'PROTECT YOURSELVES, PROTECT YOUR LOVED ONES';
'IF YOU GO OUT YOU CAN SPREAD IT. PEOPLE WILL DIE';
'VACCINATIONS PROTECT US ALL'
'STAY ALERT, CONTROL THE VIRUS, SAVE LIVES'.
A ritual was spawned that acted to showcase the good guys. At 8.00pm every Thursday evening, for 10 consecutive weeks, we were encouraged to 'Clap for Carers' so as to demonstrate our appreciation for those NHS staff and key workers courageously risking their lives on the coronavirus frontline. Neighbours stood on their door steps whooping, clapping and clanging pots and pans, smiling at each other in mass recognition of their self-righteousness; meanwhile, those who opted not to participate in this pre-orchestrated show of virtue often felt like skulking Beelzebubs by remaining indoors. The message was clear: to qualify as a laudable human being you must comply with the Government's coronavirus narrative.
Over recent weeks the ego-massaging slogans have swung into overdrive. Professor Whitty, in a TV press conference on the 21st September, said that anyone who increased their own risk of exposure 'increase the risk of everyone' around them. Health Secretary, Matt Hancock, has resorted to telling university students not to 'kill your gran'. And the unrelenting media campaign has peppered us all with a new batch of virtue-signalling statements that equate following the rules with being a good person: 'I wash my hands to protect my Nan'; 'I wash my hands to protect my family'; 'I wear a face covering to protect my mates'; and 'I make space to protect you'.
Furthermore, the 'fundamental attribution error' (mentioned above) ensures that the altruistic majority who are openly conforming with the diktats will blame any subsequent increase in coronavirus cases or deaths on those who didn't comply, while themselves taking the credit for any positive change in the statistics.
Although these ego-boosting messages claiming that compliance with coronavirus restrictions is synonymous with goodness can border on the nauseating – a bit like an acquaintance repeatedly stating what a great guy he is - the BIT psychologists know they are very effective in nudging us towards conformity.
There is, however, another motivator that is the most potent of all: fear.
It has long been recognised by psychologists that our current emotional state will significantly influence our mental processes and behaviour. This 'mood congruence effect' will result in a person selectively noticing and remembering information that is consistent with an existing mood. Thus, if I'm happy, I will be more likely to remember my past successes, to notice the positives in my current life and to develop optimistic beliefs about the future. If I'm sad, I'll display preferential access to memories of failure and loss, notice the negatives in my current life and subsequently harbour pessimistic beliefs about myself and the world. But if I'm fearful, my memory will be skewed in favour of past scary events, my attention will selectively focus on potential dangers in my current environment, and my mind will be swamped with thoughts about future threats and potential disasters; this re-calibration of our mental faculties towards fear mode has been superbly exploited by BIT psychologists to ensure mass compliance with the Government's coronavirus diktats.
The decision to scare us into submission was a strategic one. The minutes of a meeting of the Government's expert advisors (SAGE) on the 22nd March – a forum that includes psychological specialists – displays a clear intention: 'The perceived level of personal threat needs to be increased among those who are complacent' by 'using hard-hitting emotional messaging'. They knew that a frightened population is a compliant one. And haven't they delivered.
In tandem with a subservient mainstream media (that has, almost exclusively, towed the Government line), the BIT has inflicted a prolonged and concerted scare campaign upon the British public the primary aim of which has been to inflate levels of fear. Methods deployed have included:
a) Daily statistics, displayed without context: First it was the death meter, macabrely displaying the number of people who had died each day from coronavirus. This victim count was reported out of context, without any reference to the number of daily deaths from other causes or the fact that around 1600 people die in the UK each day under normal circumstances. When the COVID-19 mortality rate dipped, the statistical focus shifted, first to rates of transmission and subsequently the scarily high number of 'cases' – who can easily forget Vallance and Whitty's recent shock-and-awe presentation about the potential for 50,000 new cases per day?
b) Recurrent footage of death and dying: First it was Lombardy (the hotspot of the pandemic in Italy) with repeated screening of patients gasping for air in the Intensive Care Units. And then it was coffins piling up in the New York mortuaries or bodies littering the streets in Ecuador. Real-time images of death and dying will always be shocking, irrespective of the cause; to exclusively focus on COVID-19 deaths and not the many more victims of other illnesses is crass and grossly misleading, but calculated to exaggerate people's fear of coronavirus.
c) Scary slogans: Every media channel has continually bombarded us with fear-inducing mantras, for example:
'CORONAVIRUS: ANYONE CAN GET IT. ANYONE CAN SPREAD IT'.
To maximise the impact, the posters displaying these dire warnings have often been accompanied by images of emergency personnel wearing medical masks and visors. Even driving in our cars with the radio off doesn't protect us from this assault, as roadside warnings proclaiming 'STAY ALERT' and 'YOU ARE IN A HIGH RISK AREA' have become more common.
d) Mandatory face coverings
Once the mission to ratchet up the fear levels had been accomplished, mandatory mask wearing was introduced. Acting as a crude, highly visible indicator that danger is all around, face coverings are making a major contribution to the maintenance of the widespread hysteria. (See previous blog).
This deliberate and intensive campaign to elevate fear levels above what would be rational for the threat posed by a respiratory virus has been a remarkable success. Surveys show that UK citizens believe that coronavirus has killed around 7% of the population, a death toll that, if true, would be in excess of 4,500,000 people – at the time of writing, the official mortality figure is around 44,000. But research is not necessary to grasp how scared people are; just take a walk outside and watch pedestrians swerve off the pavement into the road to get out of your way, or hold their breath and press themselves against a wall as if you're a bio hazard.
After using messengers we respect or identify with to promote compliance-inducing fear and self-righteousness, the BIT has deployed another weapon to pound us into submission: a hefty dose of peer pressure.
Awareness of 'social norms' - the prevalent views and behaviour of our fellow citizens – can exert pressure on us to conform. We are strongly influenced by what others do; awareness of being in a deviant minority is a source of discomfort. The Government has repeatedly used normative pressure throughout the coronavirus crisis to gain the public's compliance with their escalating restrictions.
The most straightforward example is how, during interviews with the media, ministers have often resorted to telling us that the vast majority of people are 'obeying the rules'. Whether the diktat concerns social distancing, travel restrictions, or 'rule of six', Government representatives continually state that almost all of us are conforming. Although relaying details of social norms in this way can help improve compliance, ongoing repetition is required to prevent the potency of the approach decaying over time. A further disadvantage is that normative pressure is less effective in changing the behaviour of the deviant minority if there is no visible indicator of pro-social compliance rooted in communities. And this is where the BIT specialists delivered their masterstroke: mandatory masking.
In order to enhance and sustain normative pressure, people need to be able to instantly distinguish the rule breakers from the rule followers; the visibility of face coverings provides this immediate differentiation. Appearing unmasked in public places can feel comparable to not openly displaying the icon of a dominant religion while being among devout followers. Even if no explicit challenge ensues, the implicit demand to conform is palpable.
Ethically unacceptable?
Back in 2010, the authors of the 'MINDSPACE' document recognised the significant ethical dilemmas arising from the use of influencing strategies that impact subconsciously on the country's citizens. It is acknowledged that the deployment of covert methods to change behaviour 'has implications for consent and freedom of choice' and offers people 'little opportunity to opt out' (p66 – 67). Furthermore, it is conceded that 'policymakers wishing to use these tools … … need the approval of the public to do so' (p74 – my emphasis). So have the British people been consulted about whether they agree to Government using covert psychological techniques to promote compliance with contentious public health policies? I suspect not.
In recognition of the importance of gaining public permission to implement their subconscious nudges, the proponents of 'MINDSPACE' suggested several practical ways of doing so. Thus, 'focus groups' and 'citizens' juries' have been proposed (p53-54) where a small, demographically diverse range of people are brought together to express their views about a topic. However, the small scale of these events – even if they have taken place and addressed public health policy - means their conclusions cannot be seen as synonymous with a legitimate public endorsement. More ambitiously, the 'MINDSPACE' authors recommended 'deliberative forums' involving a representative sample of several hundred people brought together for a day or more to explore an issue and reach a collective decision. Has any public consultation of this type been carried out to seek permission for the widespread use of covert strategies for the purpose of gaining our compliance with public health restrictions? If so, I'm not aware of any.
Clearly, BIT specialists, along with their Government paymasters, are operating in ethically-murky waters in implementing their nudges, without our consent, to promote mass acceptance of infringements on our basic human freedoms. The British Psychological Society is the lead organisation for psychological specialists in the United Kingdom, and their Code of Ethics and Conduct (2018) describes one of its 'Statement of Values' as:
3.1 'Psychologists value the dignity and worth of all persons, with sensitivity to the dynamics of perceived authority or influence over persons and peoples and with particular regard to people's rights.
In applying these values, Psychologists should consider: … consent … self-determination.
3.3 'Psychologists value their responsibilities … to the general public … including the avoidance of harm and the prevention of misuse or abuse of their contribution to society.' [All my emphasis].
While the application of subliminal prompts to gain our cooperation with unequivocally worthwhile campaigns – for example, to stop young men stabbing each other or to reduce vandalism – would, in all likelihood, be universally acceptable to the British public, it is much more uncertain as to whether citizens would approve of their use to win our compliance with unprecedented lockdowns, travel restrictions and state diktats determining with whom we can, and cannot, mix.
And the ethical position of the behavioural psychologists becomes even more precarious when one considers the ongoing carnage associated with the elevated fear levels. The strategic decision to scare the general population (based centrally on the advice of the BIT specialists) will be responsible for the 'collateral' deaths of many thousands of people with non-COVID illnesses who, too frightened to attend hospital, are dying in their own homes at a rate of around 100 each day. There is also evidence that parents have been too scared to take their ill children to Accident & Emergency departments. Furthermore, the damage inflicted on the mental health of the nation, including escalating suicide rates, is as yet difficult to quantify but is likely to be substantial. Such is the cataclysmic responsibility of the SAGE experts who recommended fear inflation as a means of achieving compliance.
The covert strategies proposed by BIT specialists, and incorporated into the Government's coronavirus information campaign, have achieved their aim of getting the large majority of the population to obey the draconian public health restrictions. The nature of the tactics deployed – with their subconscious modes of action and the emotional discomfort generated – do, however, raise some pressing concerns about the legitimacy of using psychological techniques for this purpose. An open, public-wide debate about the ethical integrity of these approaches, and the extensive collateral damage associated with them, is now urgently required.
Behavioural Insight Team
Elevated fear
Compliance through fear
Virtue signalling
Unethical psychologists
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Who is responsible for inflicting unethical behavioural-science 'nudges' on the British people?
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redpajama_set_name: RedPajamaCommonCrawl


PARIS (Reuters) – About 20 companies including Unilever, EDF and Iberdrola joined an international alliance of 26 nations on Tuesday pledging to phase out coal to combat global warming.
At a climate summit hosted by French President Emmanuel Macron in Paris, new members of the "Powering Past Coal Alliance" agreed that traditional coal power should be phased out by 2030 in rich nations and by 2050 in other parts of the world.
The coal phase-out plan, launched last month by about 20 governments, widened on Tuesday to companies also including BT , Engie , Kering, Diageo, Marks & Spencer, Orsted , Storebrand and Virgin Group.
Nations including Sweden, Ethiopia and Latvia, as well as the U.S. state of California, also joined the alliance as part of commitments under the 195-nation Paris climate agreement reached on December 12 two years ago.
The companies committed to setting targets to end the use of traditional coal from the power sector, both for consumption and in generating electricity. Coal could play a continued role, for instance, if greenhouse gas emissions were captured and buried.
A declaration said that coal-fired power plants produce almost 40 percent of global electricity.
Most of the countries in the alliance are already cutting their use of coal and big coal users, such as China, India, the United States, Germany and Russia have not joined.
U.S. President Donald Trump plans to pull out of the Paris Agreement. He doubts that climate change is caused by man-made greenhouse gases and wants to bolster the U.S. coal and oil industries.
So let's have a look at some of the companies quoted.
I was not particularly aware that BT, Unilever, M&S, Virgin and co actually used coal for anything directly. It would be interesting though to ask them if they would like to reduce their electricity consumption by the amount that coal is contributing to the grid each day, (today it is running at 16%).
But what about energy giants EDF and Iberdrola?
In France, coal fired power is virtually insignificant, at just 1.3% last year. Two of the four coal plants there are owned by EDF, but will not last much longer, given the French Government's decision to close them down.
Interestingly it was reported in 2015 that EDF wanted to keep the coal plants at Cordemais and Le Havre open until 2035, at odds with the official state policy.
Now it appears that EDF want to take the credit for a policy imposed on them anyway.
In the UK, EDF own two coal plants, Cottam and West Burton. Again government policy is to shut these by 2025.
The rest of EDF's output in Britain and France is, of course, based around nuclear, renewables and gas, all of which stand to benefit enormously from the demise of coal.
The Spanish company Iberdrola is in a very similar situation. Currently coal power is supplying just 1.6% of total generation.
Ironically Iberdrola announced last month that it was closing its last two coal power stations in Spain because of overcapacity, but the government blocked the decision because of fears over energy security!
As with EDF, it appears that Iberdrola are pulling out of their very small coal assets because of commercial reasons.
But what about the three countries mentioned.
In Sweden, nuclear and hydro power account for 81% of generation, whilst fossil fuels only supply 1%, all of which is gas or oil.
Note that Sweden is not planning to stop using coal completely, only for producing electricity.
Without beating about the bush, Sweden's declaration is totally fraudulent, as they are using no coal at all for electricity generation in the first place.
And Latvia's position is pretty much the same.
Apart from one tiny 20MW coal/biomass co-generation, they also have no coal power generation.
Needless to say, Ethiopia also have no coal capacity either. Nearly all of their power comes from hydro.
None of these new members of the "Powering Past Coal Alliance" will make the slightest difference, as they either do not use coal, or are already phasing it out anyway.
FRANKFURT, Dec 7 (Reuters) – German utility Uniper will start up its Datteln IV hard-coal fired power station in the fourth quarter of 2018, it said in slides for an analyst and investor call on Thursday, having previously planned to start it in the first half 2018.
The 1,050 megawatts plant in western Germany has been held up for years by intense legal battles with environmentalists as Germany seeks to move away from coal-fired electricity long-term.
← Macron Saves The World!
Coal consumption in countries that are phasing out coal, vs those are NOT. The countries phasing coal out, is a very small minority of usage.
Please can you provide a citation so that I can understand where this graph comes from.
Washington State is also a polity that practices virtue signaling.
About 1990 we drove through a small town, named Zillah, in central Washington State.
At the edge of town was a large sign offering coal for domestic heating.
Today, Washington State does have some "thermal" power — waste wood/paper scraps and landfill gas. The big utility in the State imports electric power** from coal. Politicians want WA to be "coal-less" but haven't figured out how to do that. Real soon now, though.
Expect cost to consumers to go up.
**That plant has issues because of multiple owners and the operator (a partial owner) wants out. That company doesn't have the right sort of contracts for its sales compared to its co-owners. Some of these things are so complex they cannot be explained in fewer than 10 pages.
For all the good it will do them in the eyes of the green Luddites.
The major issue is that this is par of the relentless brainwashing campaign by the "Green-blob". The implication that major companies and countries are abandoning coal is all that they want to get over. It is a truly terrifying media control that allows such dishonesty to go unchallenged: ITV news last night had a similar report about saving us all from climate change and the set narrowly survived.
Big brother certainly rules now.
TPTB caused the problem, the solution could only mean more micromanaging control, it is hard, in fact very hard not to consider that, creating energy outages is a desired outcome and limiting and rationing supply is a very malicious but effective way of cowing the population and then of course others would say that children who play with matches always get hurt.
Who knows what may happen, I can't say I desire it, but the portents are not rosy – at all.
My God! The Chinese must be loving this. The West is giving in without a fight.
Last recorded Quarter Q2 2017 coal was contributing less than 2% (for the whole of 2016 coal was 8.6%. please download the data set and do your own calculation.
I worked in power cost management in a major corporation for 20+ years. I can tell you for a fact that upper management hasn't the slightest idea where their electricity comes from.


text:
\section{Introduction}
The study of novel topological  phases of matter is an extremely active research field~\cite{RevModPhys.82.3045, Ando, RevModPhys.83.1057}. Quantum Spin Hall Insulators  (QSHI) are  a remarkable example of topology at work; in these two-dimensional insulating  systems   the non-dissipative spin current carried by gapless  edge states owes its robustness to the topology of bulk bands  described by the non-zero value of the $\mathbb{Z}_{2}$ topological invariant.
The two-dimensional graphene-like lattice with  intrinsic spin-orbit coupling has been identified as a paradigmatic example of QSHI~\cite{PhysRevLett.95.146802,PhysRevB.74.195312,PhysRevB.76.045302}.
The spin-orbit helical interaction, described by a  nearest-neighbor spin-dependent complex hopping, opens a gap in the otherwise linear spectrum of the honeycomb lattice and at the same time induces a metallic behavior on the edges.

A band gap opening,   the \emph{conditio sine qua non} for the emergence of topological  features, can be achieved---at least conceptually---in different ways, not all of them with the same  topological consequences.
A gapped phase on the honeycomb lattice may be induced by modulating the tight-binding hopping amplitudes to describe different kinds of bond dimerization or by including many-body {\em e-e} interactions.
The interplay between these three types of ``gapping" interactions---spin-orbit couplings, hopping modulation and on-site {\em e-e} interaction---has been recently studied assuming the  bond dimerization that can be  associated to uniaxial strain~\cite{PhysRevB.87.205101}. Another interesting hopping modulation is the one leading to a Kekul\'e  distortion where stronger and weaker  nearest-neighbor links alternate on the honeycomb lattice  in a $\surd 3 \times \surd 3 $ arrangement. This structure turns out to be stable in the presence of
nearest-neighbor and next-to-nearest-neighbor {\em e-e} interactions~\cite{PhysRevB.81.085105,PhysRevLett.107.106402} resulting, at the mean field level, in an effective bond dimerization of a  Kekul\'e type.

In this work, we explore the combined effects of spin-orbit couplings, hopping modulation and on-site {\em e-e} interaction. We superimpose different kinds of hopping modulation on a  Kane-Mele-Hubbard model~\cite{PhysRevB.82.075106,PhysRevB.84.205121,PhysRevLett.106.100403,PhysRevB.85.115132} describing  a two-dimensional honeycomb lattice in the presence of both  spin-orbit coupling and local {\em e-e} interaction and we identify  the topological properties of this interacting system  in terms of topological invariants. This will be done by solving the many-body problem within Cluster Perturbation Theory (CPT) and extracting topological invariants from the many-body Green's function.  The goal is to clarify how the topological phases that stem from the intrinsic  spin-orbit coupling are modified by different kinds of hopping texturing and by {\em e-e} interaction.

The paper is organized as follows: in section \ref{sec1} we consider non-interacting electrons in the presence of intrinsic spin-orbit coupling and  different kinds of hopping modulation; section \ref{sec2} extends the results to the interacting case, and the last section is devoted to discussion and conclusions.

\section{Single-particle description}
\label{sec1}

In the present section we consider a honeycomb model of non-interacting electrons represented by a single particle hamiltonian with a spin-dependent hopping term
\begin{equation}
\label{kmh}
\hat{H} = \sum_{i l, i' l' s} t_{il,i'l'}(s)\hat{c}_{i l s}^{\dag} \hat{c}_{i' l'  s}~.
\end{equation}
Here $i,i'$ run over the atomic positions within the unit cell, $l,l'$ refer to lattice vectors identifying  the unit cells of  the lattice, and {\em s\,}=1,2  is for spin up and down. $\hat c^\dagger_{ils}$ and $\hat c_{ils}$ are respectively the electron creation and electron annihilation operators. The hopping term  $t_{il,i'l'}(s)$  includes both the  first-neighbor spin-independent hopping  and the Haldane-Kane-Mele
second-neighbor spin-orbit coupling~\cite{PhysRevLett.61.2015,PhysRevLett.95.146802} given by
$
\imath t_{KM} s_{z} ({d_{1}} \times {d_{2}})_{z}
$, where $d_{1}$ and $d_2$ are  unit vectors  along the two bonds that connect site  $i l$ with site $i' l'$,  and $s_z$ is the unit vector in the direction orthogonal to the lattice plane.
This hamiltonian  preserves time-reversal symmetry and parity symmetry. In turn, this implies that---by Kramer's
theorem---states come in time-reversal pairs and the Chern number computed from the bulk occupied bands
identically vanishes, and so does the charge conductivity. However the spin-conductivity may be non-vanishing as it depends upon the difference between the two spin-filtered Chern numbers~\cite{PhysRevLett.95.146802}.

We start by considering the modulation in the hopping amplitudes among nearest-neighboring sites that may arise as a consequence of a non-uniform shear strain. As shown in Ref.~\onlinecite{PhysRevB.80.045401} this corresponds to different values for the three nearest neighbor hopping parameters (Fig. \ref{geo} (a)).
\begin{figure}[h]
 \centering \includegraphics[width=8.5cm]{geometry1_mod.pdf}
  \caption{\label{geo} (Color online) Geometry of the two-dimensional (2D) honeycomb lattice with different hopping texture: (a) generalized dimerization with different nearest-neighbor hopping parameters; (b) Kekul\'e distortion. The unit cells  in the two cases, containing  two and six atoms respectively, are also shown.  Different values of second neighbor interactions are indicated.}
\end{figure}
Since the system has time-reversal and inversion symmetry we may identify the topological character of the system through the $\mathbb{Z}_2$ parity invariant  defined as the exponent $\Delta$ in the expression \cite{PhysRevB.76.045302}
\begin{align}
\label{z2}
(-1)^{\Delta} =\prod_{TRIM} \prod_{n=1}^{N} \eta_{n}(\Gamma_i)~.
\end{align}
where $\eta_{n}(\Gamma_i)= \pm 1 $ are the parity eigenvalues  of the occupied bands for any of the two spin sectors, calculated  at time-reversal invariant momenta (TRIM), and $\Gamma_i$ is defined by the condition that $-\Gamma_i= \Gamma_i +\mathcal{G}$ with $\mathcal{G}$ a reciprocal lattice vector.
The value of the $\mathbb{Z}_2$ topological invariant  distinguishes trivial insulators ($\Delta =0$, mod 2) from topological QSH insulators ($\Delta =1$, mod 2).

The eigenvalues and eigenvectors for the honeycomb lattice as well as the parity eigenvalues at TRIM points can be easily calculated analytically in terms  and hopping parameters by solving the $2\times 2$ secular problem; we obtain
\begin{eqnarray*}
  \eta_{1}(\Gamma_1) &=& 1 \\
  \eta_{1}(\Gamma_2) &=& {\rm sign}[t_1+(t_2-t_3)] \\
  \eta_{1}(\Gamma_3) &=& {\rm sign}[t_1-(t_2-t_3)] \\
  \eta_{1}(\Gamma_4) &=& {\rm sign}[t_1-(t_2+t_3)]
\end{eqnarray*}
where the $t_i$ are the three (generically different) hopping parameters. For the  $\mathbb{Z}_2$  invariant we thus have
\begin{equation}
\label{inv_gg}
(-1)^{\Delta} = {\rm sign} \left[ t_{1} - \left( t_{2} + t_{3} \right) \right] {\rm sign} \left[ t_{1}^{2} - \left( t_{2} - t_{3} \right)^{2} \right]
\end{equation}

Interestingly, these quantities depend just on first near- est neighbor hopping parameters and not on second nearest neighbor hoppings describing spin-orbit interaction.
This is a direct consequence of symmetry: each site in the unit cell is connected to 3 pairs of second nearest neighbors sharing the same distance but placed in opposite directions (sites 1-2, 3-4, 5-6 in Fig. \ref{geo}). For this reason the Hamiltonian matrix $H(k)$ at any TRIM  point  does not depend on  Haldane-Kane-Mele second-neighbor spin-orbit coupling. We have in fact
\begin{equation*}
H(k) = \left(
\begin{array}{cc}
g(k) & -f(k)  \\
-f(k)^* &  - g(k)
\end{array}
\right)
\end{equation*}
where
\begin{eqnarray*}
g(k) &=& 2[t_{KM} \sin(k_y ) \\  \nonumber
     &-& t'_{KM} \sin(k_x \sqrt{3}/2+k_y /2)  \\  \nonumber
     &-&  t''_{KM} \sin(- k_x\sqrt{3}/2+ k_y /2)] \\  \nonumber
f(k) &=&  t_1 \exp(\imath k_x / \sqrt{3}) \\  \nonumber
     &+& \exp[-\imath k_x /(2 \sqrt{3}) ]  [t_2  \exp(- \imath  k_y / 2)  + t_3  \exp(\imath k_y / 2)].
\end{eqnarray*}
It is then easy to check that $g(k)$ at any TRIM  point is identically zero.
Still, the spin-orbit interaction is essential in order to obtain a non-trivial topological behavior: for $t_{KM}= 0$ a modulation in the hopping parameters would only transform a semi-metal into a trivial insulator while for $t_{KM}\neq 0$ the system is  always an insulator  (except just at the phase boundary---see below). For $t_{KM}\neq 0$, by tuning the hopping parameters $t_i$  we may go from a trivial insulating phase to a topological Quantum Spin Hall insulating regime. The values where a phase transition occurs---either between QSHI and topologically trivial insulator (TTI) for $t_{KM}\neq 0$ or between semimetal and TTI for $t_{KM}= 0$---are identical and the phase diagram that we obtain  (Fig.~\ref{dimer_nonint} (a))  coincides, as far as the phase separations are concerned, with the one reported in refs.~\onlinecite{PhysRevB.80.045401,PhysRevB.74.033413} for $t_{KM}= 0$. We observe that right at the transition  between QSHI and TTI phases the single particle  gap $\Delta _{sp}$ closes down  and the system recovers a semi-metallic behavior. We analyze in particular the behavior of the system varying just one hopping parameter ($t_2$) with $t_{KM}=t'_{KM}=t''_{KM}$,  moving in the parameter space along the line shown  in Fig.~\ref{dimer_nonint} (a) where  $t_3=t_1 $. For this choice of parameters the gap between filled and empty states evolves as shown in Fig.~\ref{dimer_nonint} (b). Before the transition, the absolute value of the energy gap depends on $t_{KM}$ but after the transition it becomes independent on $t_{KM}$ and  increases linearly as $ E_{g} = 2 \left( t_{2} - 2 t_{1} \right)$.

In the lower panel of Fig.~\ref{dimer_nonint} we show   the evolution of the band structure assuming $t_{KM}=t'_{KM}=t''_{KM}$ and   $t_{KM}/t_1= 0.1$ along the line in parameter space  where $t_{1} = t_{3} $. By increasing the value of $t_{2}$ the positions in k-space of the  band gap  move along a line parallel to $k_{y} = \frac{1}{\sqrt{3}} k_{x}$ and merge at M points where the gap closes down for $t_{2}/ t_{1}=2$, signaling the topological transition from QSHI to TTI. We stress again that  the spin-orbit term, even including a modulation in second-neighbor hopping interaction,   does not alter the  parity symmetry ($C_2$) and as such it does not affect the gap position in k-space.  After the transition the gap remains at M.

We turn now to the Kekul\'e distortion. In this case  the unit cell contains six atoms, with alternating values in  the nearest-neighbor hopping parameters $t $ and $t'$  as shown in Fig. \ref{geo} (b). In principle we   have  two possible values of the second nearest-neighbor parameters; since their dependence on the lattice deformation is not easy to assess we have considered two separate cases, namely $t'_{KM}=t_{KM}$ and $t'_{KM}=t'/t \times t_{KM}$ as suggested in Ref.~\onlinecite{PhysRevB.85.205102}.

Neglecting at first the variation in the second nearest-neighbor hopping parameters we notice that the minimum separation between filled and empty states  is, for any value of $t'/t$ and $t_{KM}/t$, pinned at a $\Gamma$ point. This is  shown in the lower panel of Fig. \ref{kekule0} where the dispersion of the highest occupied band is shown for different values of $t'/t$ and for $t_{KM}/t=0.1$. This remains true also for  $t'_{KM} \neq t_{KM}$. We may then identify  the analytic dependence of the $\mathbb{Z}_{2}$ invariant on the hopping parameters by considering the eigenvalues at the $\Gamma$ point only, where the diagonalization of the $6 \times 6 $ Hamiltonian matrix is trivial, and look for the conditions that guarantee a zero gap between filled and empty states. Indeed  in the non-interacting case the transition from a trivial to a non-trivial topological phase requires the gap to close down.
The six eigenvalues at $\Gamma$ ($e_1=-t-2t'$, $e_2=t+2 t'$, $e_3=t-t'-  \sqrt{3} (t_{KM}+2 t'_{KM})$, $e_4=-t+t'- \sqrt{3} (t_{KM}+2 t'_{KM})$, $e_5=t-t'+ \sqrt{3} (t_{KM}+2 t'_{KM})$, $e_6=-t+t'+ \sqrt{3} (t_{KM}+2 t'_{KM})$) are easily obtained from the hamiltonian matrix
\begin{equation}
H_{\uparrow} (\Gamma) = \left(
\begin{array}{cccccc}
0 & -t' & m  & -t & m^* & -t' \\
-t' & 0 & -t' & m  & -t & m^* \\
m^* & -t' & 0 & -t' & m  & -t \\
-t & m^* & -t' & 0 & -t' & m \\
m & -t & m^* & -t' & 0 & -t' \\
-t' & m & -t & m^* & -t' & 0
\end{array}
\right)
\end{equation}
where $m=\imath (2 t'_{KM}+t_{KM})$. Therefore the gap closure occurs when one of the following two conditions is verified
\begin{equation}
\begin{split}
& t-t'- \sqrt{3} (t_{KM} +2 t'_{KM})= 0 \\
& t-t'+\sqrt{3} (t_{KM} +2 t'_{KM}) = 0
\end{split}
\end{equation}
This leads  to the following analytic expression for the $\mathbb{Z}_{2}$ invariant as a function of the hopping parameters:
\begin{equation}
\label{inv_kek}
(-1)^{\Delta} = {\rm sign} \left[ \left(t-t' \right)^{2} - 3 \left( t_{KM}+2 t'_{KM} \right)^{2} \right]~.
\end{equation}
This relation has been checked numerically in terms of  parity eigenvalues according to eq.~\eqref{z2}. We obtain in this way the  phase  diagram of Fig. \ref{kekule0} (a): any $t_{KM}\neq0$ defines a range of    $t'/t $ where the system behaves as a QSHI, and this range depends on the strength of the spin-orbit coupling. The hopping modulation has different effects if $t_{KM}=0$ or $t_{KM}\neq 0$  as shown in Fig. \ref{kekule0} (b) where the evolution of the gap value is reported  for $t_{KM}=t'_{KM}$: for the undistorted system in particular we have  zero gap and  maximum gap for $t_{KM}=0$ and $t_{KM}\neq 0$, respectively. Notice that  the analytic expression of the $\mathbb{Z}_{2}$ invariant allows us to obtain quite simply the phase diagram also in the case of $t'_{KM}\neq t_{KM}$ and that for $t'_{KM}=t'/t \times t_{KM}$  we recover the results~\footnote{Notice that  for $t'_{KM}=t'/t \times t_{KM}$  we plot  $1/\alpha$ vs $\lambda$, with $\alpha \equiv t / t'$, $\lambda\equiv t_{KM}/t = t'_{KM}/t'$  while  in Ref. \onlinecite{PhysRevB.85.205102} the corresponding phase diagram is  $\alpha$ vs $\lambda$ } of Ref.~\onlinecite{PhysRevB.85.205102}.

\section{Effects of  {\em e-e} correlation}
\label{sec2}
The Kane-Mele-Hubbard model \begin{align}
\label{kmh_int}
\hat{H} = \sum_{i l, i' l' s} t_{il,i'l'}(s)\hat{c}_{i l s}^{\dag} \hat{c}_{i' l'  s} +
U \sum_{i l} \hat{c}_{i l \uparrow}^{\dag}\hat{c}_{i l \uparrow}\hat{c}_{i l \downarrow}^{ \dag}\hat{c}_{i l  \downarrow}~,
\end{align}
where  on-site {\em e-e} repulsion is added to the non-interacting hamiltonian of eq.~\eqref{kmh}, is a paradigmatic example of an interacting topological insulator~\cite{Assaadrev,doi:10.1142/S0217984914300014}.  In this case, in order to topologically characterize the system, we face two distinct problems: on one side we need to substitute the single particle band structure with the quasi-particle excitation energies that can be obtained from the many-body Green's function; on the other side we must  extend the $\mathbb{Z}_{2}$ parity invariant, originally associated to a single particle state, to the interacting case. In Refs.~\onlinecite{PhysRevB.85.165126,PhysRevX.2.031008} it has been demonstrated that the $\mathbb{Z}_{2}$  invariant is determined by the behavior of the one-particle propagator at zero frequency only:
the inverse of the Green's function at zero frequency defines a fictitious  noninteracting topological hamiltonian \cite{0953-8984-25-15-155601}
\begin{align} h_{topo}(k)\equiv -G^{-1}(k,0)
\label{htopo}
\end{align}
and its eigenvectors
\begin{align}
\label{eigen}
h_{topo}(k)|k,n\rangle = \epsilon_{n }(k)|k,n\rangle
\end{align}
are the quantities that in eq.~\eqref{z2} replace the non-interacting band eigenvectors to obtain the topological invariant for the interacting system.

These concepts have been recently applied to identify the topological character of heavy fermion mixed valence compounds~\cite{PhysRevB.88.035113,PhysRevLett.111.176404,PhysRevLett.110.096401,PhysRevB.87.085134} and of the half-filled honeycomb lattice~\cite{grandi} also in the presence of uniaxial  bond dimerization~\cite{PhysRevB.87.205101}.

In order to solve the eigenvalue problem~\eqref{eigen}, in strict analogy with what is done in any standard Tight-Binding scheme for non-interacting hamiltonians, a Bloch basis  expression of the topological hamiltonian, namely, of the dressed Green's function and of its inverse, is required:
\begin{align}
\label{gij}
 G_{ij}(k, \omega)=\langle \Psi_0|\hat{c}_{k  i }^{\dag}\hat{G} \hat{c}_{k j}|\Psi_0 \rangle
 + \langle \Psi_0|\hat{c}_{k  i }\hat{G} \hat{c}_{k j}^{\dag}|\Psi_0\rangle
\end{align}
where $\hat{G}=\frac{1}{\omega-\hat{H}}$
and
\begin{align*}
\hat{c}_{k i}^{\dag}=\frac{1}{\sqrt{L}}\sum_{l}^{L} e^{-i k\cdot(R_l+r_i)}\hat{c}_{l i }^{\dag} \, ; \ \ \hat{c}_{k i}=\frac{1}{\sqrt{L}}\sum_{l}^{L} e^{ik\cdot(R_l+r_i)}\hat{c}_{l i }
\end{align*}
with $R_l$ the  lattice vectors ($L$ $\rightarrow \infty$) and $r_i$ the atomic positions inside the unit cell.

\onecolumngrid
\begin{center}
\begin{figure}[bth]
 \centering \includegraphics[width=17cm]{dimer_nonint.pdf}
  \caption{\label{dimer_nonint} (Color online) Upper panel: (a) Phase diagram for Kane-Mele model of the honeycomb lattice assuming the  generalized bond dimerization of Fig. 1 (a). The two phases, QSHI and TTI, correspond to different values of the $\mathbb{Z}_2$  invariant ($\Delta=1$ and $ \Delta=0$ respectively, see text).  (b) Gap value as a function of the hopping parameter $t_2$  assuming $t_{1} = t_{3}=1, t_{KM}=t'_{KM}=t''_{KM} $. Continuous line  is for $t_{KM}/t_1=0.1$, dotted line for $t_{KM}/t_1=0.3$. Lower panel:  Density plots of the occupied energy states as a function of k-point with $t_{KM}=0.1$. The evolution of the band structure is considered for $t_{KM}=t'_{KM}=t''_{KM} $ in a subset of first nearest neighbor hopping parameters with $t_{1} = t_{3}=1 $ indicated as blue dots in panel (a): $t_{2}=1 $ (c), $t_{2}=1.2 $ (d),  $t_{2}=2 $ (e) , $t_{2}=3 (f) $. In the color scale, red indicates zero gap. Brillouin zones (thin red dotted lines) and high symmetry points are also shown.}
\end{figure}
\end{center}
\twocolumngrid

Here we calculate the dressed Green's function by  Cluster Perturbation Theory  (CPT) \cite{Senechal}. CPT   belongs to the class of Quantum Cluster theories\cite{RevModPhysQC} that solve the problem of many interacting electrons in an extended lattice by a  \emph{divide-and-conquer } strategy, namely by solving first the many body problem in a subsystem of finite size and then embedding it within  the infinite medium. Different Quantum Cluster approaches (Dynamical Cluster Approach \cite{DCA}, Cellular Dynamical Mean Field Theory  \cite{Senechal_CDMFT,PhysRevLett.110.096402}, and Variational Cluster Approaches \cite{VCA}) differ for the embedding procedure and/or for the way the lattice Green's function---or the corresponding self-energy---is expressed in terms of the cluster one. The common starting point is  the choice of the $M$-site cluster used to \emph{tile} the extended lattice.
By construction CPT is exact in the two limits
$U/t=0$ (non-interacting band limit), $ U/t =\infty$ (atomic limit); for intermediate values of $U/t$ it opens a gap in metallic systems at half occupation \cite{ManghiMnO}.

\onecolumngrid
\begin{center}
\begin{figure}[bth]
 \centering \includegraphics[width=17cm]{kekule1_nonint.pdf}
  \caption{\label{kekule0}  (Color online) (a) Phase diagram for the 2D honeycomb lattice with Kekul\'e distortion showing the topological behavior  as a function of nearest neighbor modulation $t'$ and spin-orbit coupling $t_{KM}$. The grey area corresponds to $t'_{KM}=t_{KM}$ while the dashed line is the phase separation for $t'_{KM}= t'/t \times t_{KM}$.  (b) Gap value as a function of the hopping parameter $t'$  for different values of $t'_{KM}=t_{KM}$ as indicated in the inset.  Lower panel: Density plots of the occupied energy states as a function of k-point with $t'_{KM}=t_{KM}=0.1$. The evolution of the band structure is considered in a subset of first nearest neighbor hopping parameters ( $t'/t=1 $ (c), $t'/t=1.5 $ (d),  $t'/t=2 $ (e)) indicated as blue dots in panel (a). In the color scale, red indicates zero gap. The reduced Brillouine zone for the 6-site unit cell (thin red dotted line) and high symmetry points are shown.}
\end{figure}
\end{center}
\twocolumngrid

In CPT,  Green's function (\ref{gij}) for the extended lattice is calculated by solving the equation
\begin{equation}\label{QC}
G_{i j}(k,   \omega)=G^c_{ i j}(  \omega)+ \sum_{i'}^M B_{i i'}(k,  \omega) G_{i' j}(k,   \omega).
\end{equation}
Here $G^c_{ i j}$ is the cluster Green's function in the local basis obtained by exact diagonalization of the interacting hamiltonian for the finite cluster; we separately solve the   problem for  $N$, $N-1$, and $N+1$ electrons and
express the cluster Green's function in the Lehmann representation at real frequencies.

The matrix $B_{i i'}(k,\omega)$ is given by
\begin{align*}
B_{i i'}(k,\omega)= \sum_l^L e^{i k\cdot R_l} \sum_{i''}^M G^c_{i i''}(\omega) t_{i'' 0, i' l}(s)
\end{align*}
where $t_{i''0 ,i' l}$ is the hopping  between site $i'$ and $i''$ belonging to different clusters.

The key approximation here is the expression of  the complete Green's function in terms of Green's functions of decoupled clusters and it is important to verify the accuracy of the results by using larger and larger cluster sizes. This procedure is limited by the dimensions of Hilbert space  used in the exact diagonalization, dimensions that grow exponentially with the number of  sites. A further limitation in the cluster choice arises by a symmetry requirement since only clusters that preserve the point group symmetries of the lattice must  be used.~\cite{RevModPhysQC,grandi} The role of symmetry in Quantum Cluster approaches is complex:  the extended system is described as a periodic repetition  of correlated units and   the translation periodicity  is preserved only  at the superlattice level. In the  honeycomb lattice where the Dirac cones are the consequence of  perfect long-range order,  theories based on Quantum Cluster schemes, such as CDMFT, VCA, and CPT, regardless of them being variational or not, and independent on the details of the specific implementations (different impurity solvers, different temperatures),   at $t_{KM}=0$  give rise to a spurious  excitation gap  for  $U \rightarrow 0$. The only exception is the Dynamical Cluster Approach  (DCA)  that  preserves by construction translation symmetry and has been shown to describe better the small $U$ regime; DCA becomes, however, less accurate at large $U$  where it overemphasizes the semimetallic  behavior of the honeycomb lattice.~\cite{PhysRevB.87.205127} In this sense DCA and the other Quantum Cluster approaches can be considered as complementary and it would be interesting to compare their results also for the distorted honeycomb lattice.
Another strategy has been proposed that seems to overcome this shortcoming,  providing for the undistorted honeycomb lattice  a semimetal behavior up to some finite $U$.~\cite{PhysRevB.90.165136} The strategy consists in  choosing clusters  that break  the lattice point $C_6$ symmetry (8- and 10-site clusters).  The quasiparticle band dispersion that is obtained in this way is, however, unphysical: quasiparticle energies at $k$ and $Rk$, $R$ being a point group rotation, turn out to be different,  violating a very basic rule of band structure.~\cite{grandi}  And it is just this violation that makes the system semimetallic at finite $U$ since the gap closes at a $k$-point but not at its rotated counterpart. For this reason  breaking the rotational symmetry is not an allowed strategy to correct the erroneous insulating phase.

We have checked the dependence of our results on the cluster size by comparing the case of the generalized dimerization results obtained for 2- and 8-site clusters;   we have verified that no significant changes occur in the spectral functions  and for this reason we report results obtained only for the smallest cluster size, namely, 2- and 6-site clusters for the  generalized bond dimerization  and Kekul\'e distortion, respectively. Notice that in this case the clusters used to ``tile" the infinite lattice are those shown in Fig. \ref{geo} and that $t_1$ ($t'$) describe intra-cluster hoppings for the two distortions (generalized dimerization and Kekul\'e,  respectively).
Eq.~\eqref{QC} is  solved  by an $M\times M$  matrix inversion at each $k$ and $\omega$.
A second $M\times M$ matrix inversion is needed to obtain the topological hamiltonian according to eq.~\eqref{htopo}. The topological hamiltonian is then diagonalized and its  eigenvectors are used for the calculation of    $\mathbb{Z}_2$ according to~\eqref{z2}.

It is worth recalling that  the eigenvalues of $h_{topo}$ used to calculate the value of the $\mathbb{Z}_2$  invariant in principle have nothing to do with the quasi-particle excitation energies: they only  contain topological information and the full Green's function is needed to calculate quasi-particle spectral functions
\begin{align}
\label{akn}
A(k,\omega) = \frac{1}{\pi}\sum_n {\rm Im}\,  G(k,n,\omega)
\end{align}
where
 \begin{align*}
G(k,n,\omega) =  \frac{1}{M}\sum_{i i'} e^{-i k \cdot(r_i-r_{i'})}\alpha^{n*}_i(k) \alpha^n_{i'}(k)  G_{i i'}(k,\omega)
 \end{align*}
with $n$ the band index and $\alpha^n_i(k)$ the eigenstate coefficients obtained by the single-particle band calculation.~\cite{ManghiMnO}
Spectral functions   can also  be used to identify topological properties,  looking for the existence of gapless quasiparticle states in one-dimensional (1D) honeycomb ribbons.  The energy broadening necessarily  involved in the calculation of spectral functions makes this procedure  less accurate than the calculation of the ${\mathbb Z}_2$ invariant based on $h_{topo}$ eigenvectors: in $G^{-1}$ no energy broadening is required and  the boundaries in the phase diagram are sharply identified.

Fig. \ref{akn_fasi_int}  shows the results that  we obtain for  interacting electrons in the honeycomb lattice  with the two kinds of hopping modulation (generalized dimerization and Kekul\'e distortion).     By comparing the interacting case and  the non-interacting one we notice that  the QSHI/TTI phases are modified by the local {\em e-e} interaction for both lattice distortions. In the  case of generalized dimerization   (Fig. \ref{akn_fasi_int} (a))  the overall region in parameter space where the system is in the QSHI phase  increases with $U$ but at the cost of larger distortions: when on the contrary the system is almost undistorted (lower corner on the left of Fig. \ref{akn_fasi_int} (a), where $t_2$ and $t_3$ are closer to $t_1$) the effect of {\em e-e} is to extend the region of the TTI phase. For $U\geq 3.5$ the undistorted system is always topologically trivial.

The phase separation lines remain linear and independent on the strength of spin-orbit coupling, as in the non interacting case. Indeed, the effect of {\em e-e} interaction is to induce a  renormalization of the intra-cluster hopping parameters and therefore the topological hamiltonian of eq.~\eqref{htopo} coincides with an effective single-particle hamiltonian with modified hopping terms. This is particularly evident when a 2-site cluster is used as a basic unit in CPT, but remains true with larger clusters. We have checked this   by considering an 8-site cluster and we do not find significant differences.

In the Kekul\'e distortion, as expected from the previous analysis for the non-interacting case, different results are obtained assuming $t'_{KM}= t_{KM}$ or  $t'_{KM} \neq t_{KM}$. However in  both cases  the effect of {\em e-e} interaction favors  even more clearly the TTI phase since the total area where the system behaves as a QSHI is reduced with respect to the non-interacting case and, for a given distortion, larger values of spin-orbit coupling are required to have a non trivial topological character~\cite{Note1}.

The lower panels of Fig. \ref{akn_fasi_int}   show  the spectral functions  that we obtain for the two kinds of hopping modulation  as a function of the intra-cluster hopping parameters ($t_1$ and $t'$ respectively) at  fixed values of Hubbard $U$ and of inter-cluster hopping parameters $t'_{KM}=t_{KM}$ ($t_2=t_3=1$ and $t=1$ in the two cases respectively). We notice that the hopping modulation induces in both cases a closure of the energy separation between filled and empty quasi-particle states, signaling the topological phase transition.

\onecolumngrid
\begin{center}
\begin{figure}[tbh]
 \centering \includegraphics[width=18cm]{akn_fasi_mod.pdf}
  \caption{\label{akn_fasi_int} Phase diagram  and spectral functions for the Kane-Mele model of the honeycomb lattice in the presence of on-site {\em e-e} interaction for  the generalized bond dimerization (left) and for the Kekul\'e distortion (right panel). Panel (a): phase diagrams for the generalized bond dimerization obtained with different values of $U$  as a function of $t_2$ and $t_3$ at $t_{KM}=0.1$. Panels (b)--(d): spectral functions for the dimerized honeycomb lattice with  $t_{KM}=0.1$, $U=3$,  $t_2=t_3=1$, and (b) $t_1=1$, (c) $t_1=1.5$, and (d) $t_1=2$.
  Panel (e): phase diagram for the Kekul\'e distortion   at a fixed value $U=3$ as a function of $t'$ and $t_{KM}$.  The filled area corresponds in both cases to the non interacting result reported in Figs. \ref{dimer_nonint} and \ref{kekule0}. The dashed line  indicates the phase separation for for $t'_{KM}= t'/t \times t_{KM}$. In blue and red are reported the results assuming $t'_{KM}=t_{KM}$ and $t'_{KM}=t'/t \times t_{KM}$, respectively. Panels (f)--(h): spectral functions for the  honeycomb lattice in the Kekul\'e distortion with $U=3$,  $t=1$, $t'_{KM}=t_{KM}$, and (f) $t'=1$, (g) $t'=1.3$, and (h) $t'=2$.  }
\end{figure}
\end{center}
\twocolumngrid

\section{Conclusions}
\label{sec3}

We have studied the joint effects of intrinsic spin-orbit coupling, hopping modulation and on-site {\em e-e} interaction on the topological properties of the 2D honeycomb lattice. The goal was to understand how the topological phases induced by  intrinsic  spin-orbit coupling are modified by different kinds of lattice distortions and by {\em e-e} interaction.
The main results may be summarized as follows.
In the non-interacting case the shape of the phase diagram obtained assuming a generalized dimerization  does not depend on the value of the intrinsic spin-orbit coupling: the phase separation lines are identical for any value of $t_{KM}$,  with the noteworthy difference that in the parameter range where the system is for $t_{KM}=0$  a semi-metal, for   any other $t_{KM}\neq 0$  the system  is  a QSHI. In the absence of spin-orbit coupling the Kekul\'e distortion makes the system insulating and in this case the parameter space where the system behaves as a QSHI increases with  the value of $t_{KM}$.

We have extended the analysis in terms of topological invariants to the case of interacting electrons by calculating the dressed Green's function within CPT and the topological hamiltonian. For both lattice distortions, in the regime of relatively small deformations,  the effect of {\em e-e} interaction is to reduce the region where the system behaves as a QSHI.  In this sense we may conclude that  lattice distortions  and  {\em e-e} interaction do not cooperate in inducing a non trivial topological phase but rather reduce the possibility of finding the honeycomb lattice in a non-trivial topological state.

redpajama_set_name: RedPajamaArXiv


In 2017 over 9000 dogs were vaccinated during the Laikipia Rabies Vaccination Campaign. This year, the campaign will held over 8 weekends in months of October and November and targets 15,000 animals.
In 2015, the first Laikipia Rabies Vaccination Campaign (LRVC) vaccinated a total of 821 domestic dogs and cats. That number and coverage has since increased with last year's efforts reaching over 9,000 dogs and cats in the county.
The 2018 LRVC plans to widen its scope reaching out to more communities by returning to areas where vaccination has previously taken place and expanding coverage into new communities to get the numbers to 15,000. Is it possible? Absolutely!
We, as Laikipians, can work together to eradicate this deadly virus. With dedicated partnerships with the local residents, County Government and LRVC partners, we can contribute to making Laikipia, Kenya's first rabies free county.
The LRVC, in partnership with the Laikipia County Government, will run for 8 weekends in the months of October and November. The campaign's focus is in rural communities, which have the greatest risk of rabies exposure as well as the least access to rabies vaccination and treatment. However, this year the campaign will also include semi-urban centres with relatively large dog populations, such as Nanyuki.
In Kenya, the majority of annual rabies-related deaths occur where vaccination programs are limited or non-existent, generally where low income communities reside. In Laikipia specifically, we know that there are significant numbers of undocumented rabies cases in domestic animals, wildlife and humans annually.
If we take informed steps, we can eradicate rabies from domestic dog populations in Laikipia County in an effort towards accomplishing Kenya's 2030 vision of being an entirely rabies free nation. We will however not be able to reach this goal without your help.
Your support is crucial to our efforts. The number of students, vets and community members who are always willing to volunteer is always encouraging but we do need more financial support.
Rabies is an almost invariably fatal disease for both humans and animals. It has been shown that mass vaccination of domestic dog is the most effective way to end the Rabies virus cycle in-step towards eradication. Vaccination of domestic animals therefore is a critical step that we should all participate in for the protection of domestic animals, our already fragile wildlife population and most importantly, public health.
Together, we can eradicate rabies in Laikipia!


text:
Southend United assistant manager Dave Penney, of Castleford, charged with assaulting a police officer
Published: 13:52 Wednesday 27 May 2015
Southend United's assistant manager Dave Penny has been charged with assaulting a police officer following an incident hours before the team's bus parade promotion celebrations.
Mr Penney, 50, of Lower Oxford Street, Castleford, is also accused of assault and criminal damage in connection with the incident that happened at around 3am on Sunday.
The former Doncaster Rovers manager was arrested outside a casino as players and officials celebrated the club's promotion from League Two.
An Essex police spokeswoman said he will now appear before Southend Magistrates' Court on June 8.
Southend United held an open-top bus parade through the town on Monday after winning the League Two play-off final against Wycombe Wanderers at Wembley on Saturday.
Wakefield store at centre of tobacco raid appeals against booze licence call
The lost pubs of Wakefield - how many of these do you remember?
Police rush to incident in Wakefield city centre
New gallery of old pictures showing Wakefield schools through the years
Castleford's longest-serving market trader closes shop after 120 years due to council's 'stubborn' policies
Heartbroken young parents speak out after baby Harrison 'born sleeping' just before Christmas
More from Wakefield Express


Vector is a new Facebook game from Nekki, developer of the impressive and visually-striking one-on-one combat game Shadow Fight. The new game makes use of the same distinctive "silhouette" aesthetic in a whole new gameplay context — in this case, freerunning/parkour.
In Vector, players take on the role of a shadowy figure who is constantly being pursued by another shadowy figure. No context is given for why these two are chasing each other despite the fact that the game refers to its main sequence of levels are "story" mode, but it doesn't really matter — Vector isn't a game that's attempting to tell a complex story. Rather, it's a game that attempts to get players wrapped up in the thrill of a movie-style rooftop chase scene — and in that respect, it succeeds admirably.
Controlling Vector is very simple. Tapping the up arrow key on the keyboard causes the player character to jump; tapping the down arrow causes the player to slide under low obstacles. When glowing right-facing arrows appear on the course, the player may also press the right arrow key to enjoy a brief boost of speed — in many instances, this increase in velocity is necessary to clear some big jumps. The game is not an "endless runner" — it is split into discrete levels rather than infinite randomly-generated challenges, so it is possible to learn the best route to victory.
The bare minimum the player has to do to complete a level is survive. This gets very difficult very quickly, providing a significant challenge to even the most skilled platform gamers, but the fact that it's possible to immediately restart a level makes failure less painful. Once the player has successfully managed to traverse a level without falling into a bottomless pit or being caught by the pursuing figure, they can then concentrate on trying to achieve the elusive "three star" rating. This is achieved by collecting all of the bonus items scattered through the level and completing all of the marked "tricks" at specific points. Completing a trick is a simple matter of tapping the up arrow while passing over a trick icon, but there's a twist — the player character only knows a few tricks at the start of the game, and the remainder must be purchased using in-game currency. This may either be earned simply by playing levels or acquired through in-game purchase using Facebook Credits.
The in-game currency may also be spent on a number of other items besides the tricks — "gadgets" are effectively paid cheats, allowing players to make a level considerably easier by either removing the pursuing guard or slowing down time, while costume items allow for a limited degree of visual customization of the player character, though are relatively expensive. It's possible to have a satisfying experience with the game without spending a cent, but acquiring all of the tricks will probably require a degree of "grinding" earlier levels repeatedly in order to earn enough money.
Vector is an impressive game in all respects. It's visually stunning — the animation in particular is unlike anything else on Facebook (with the exception of Nekki's previous title Shadow Fight) — and the gameplay is solid, though the focus on realistic animations can mean the controls occasionally feel a little sluggish to respond. There's a strong sense of progression through the game, plenty of content to unlock and a robust monetization strategy in place. The only thing it's really missing is a more solid suite of social features — at present, the only thing players can do with friends is compare how many stars they have achieved. A number of features on the game's main menu are listed as "in development," though, so it's entirely possible that this aspect will be improved over time. As it stands, however, Vector is a great game that deserves to enjoy some success.
At the time of writing, Vector has 360,000 monthly active users and 60,000 daily active users. Follow its progress with AppData, our traffic tracking service for social games and developers.
Visually stunning and highly playable — another great title from Nekki.


Welcome to Jerseygirlweb, my name is Sue! I was born and raised in New Jersey. I joined the military for a few years and have always lived within the US but NJ has always been my home base. What I like about this state is that during the summer there are plenty of seasonal activities (beach, kayaking, parasailing, going to the boardwalk, etc.). During non-summer months, I can take day trips because of it's proximity to other metropolitan cities (NYC is about 1 hour away, Philadelphia is 1.5). I started this blog to promote my business http://www.thepinkbarn.com but am quickly having fun with it by discussing fashion. I try to be frugal with my clothes purchases (who doesn't like a sale?) so mostly everything you see here will be inexpensive.


Some corporate venture funds back biotechs for a strategic position, and others to feed the innovation ecosystem. Either way, the money flow from these big pharma divisions has followed that of investment in general over the past few years – namely, into oncology research.
That said, the corporate VCs have taken their feet off the oncology accelerator, an analysis by Vantage shows. Making a surprising surge since 2015 is corporate VC interest in companies working on central nervous system projects, perhaps reflecting the risky nature of drug development in this area and the need for patient investment.
This analysis measures activity by the number of rounds in which corporate VCs have participated by therapy areas for the decade ending 2018. There are signs that in general big pharma has backed away from this avenue of investment, as ready money is available from traditional VCs and the valuations of many assets continue to surge (Are the big corporate venture arms retreating?, February 18, 2019).
Corporate VC funding in oncology has followed a similar pattern: the sector hit its peak in 2016 with 27 corporate VC rounds, before this fell to 23 in 2018. This is by no means a massive retrenchment – oncology is seen as a fruitful place to put R&D money as regulatory and commercial barriers remain low.
And cancer did dominate corporate venture investment during the 10-year period analysed, with the big names participating in 197 rounds, more than double that of the next biggest biopharma therapy area. Nevertheless, corporates might be starting to view other therapy areas as more attractive as investors of all stripes have crowded into cancer research.
Enter CNS. This is a high-risk therapy area owing to failures of trials of projects targeting pain and mental health disorders, and thus biotechs working in this area generally need more time and private money to reach milestones like licensing deals and initial public offerings.
As oncology rounds backed by big pharma VCs have receded, CNS rounds have increased steadily, from six in 2015 to 14 in 2018. The CNS-focused companies that received big pharma venture backing in 2018 included Cadent Therapeutics, which has a lead project in essential tremor and is backed by Novartis; Minoryx Therapeutics, which has a project in adrenoleukodystrophy that earned Roche's support; and Alector, a dementia and Alzheimer's specialist whose crossover round included Abbvie, Amgen and Lilly. Alector went public earlier this month.
Big pharma venture divisions have shown declining interest in companies working in immunomodulators and systemic anti-infectives. In the case of the former, the big disease areas like rheumatoid arthritis are fairly well served with agents approaching the end of their market exclusivity. In the case of the latter, while governments have provided incentives to develop infectious disease drugs the fact that these agents that are seldom used remains problematic commercially.
Novartis, the most prolific corporate venture investor of the past decade, has only led four rounds in the anti-infectives area out of a total of 43. By comparison, the group led 13 funding rounds for private oncology companies.
Novartis spread the wealth, however, leading venture investments across a broad spectrum of areas including respiratory, blood, sensory organs and CNS. In breadth, the Swiss group is matched by Glaxosmithkline's SR One venture arm, which led at least one funding round in all of the same areas, but was less prolific, leading only 28 rounds in total.
Johnson & Johnson was the third-biggest leader of VC rounds over the past decade, although it has focused more on medical devices thanks to its DePuy Synthes and Ethicon medical technology subsidiaries. The New Jersey-based conglomerate led 16 rounds in the 2009-18 period, nine of which were medtech; only two were in oncology.
Some biopharma observers have lamented the sector's heavy investment in oncology because it neglects other therapy areas with unmet needs. While the corporate venture arms have been a part of this trend, signs that CNS-focused companies are getting more love should be welcomed.