text:
\section{INTRODUCTION}
The field of quantum information processing experiences a mammoth growth
in the last two decades \cite{Amico,HorodeckisRMP,Guuhne}.
Entanglement emerges as the most useful quantity among the
quantum correlations through an extensive investigations in this field.
Vast amounts of works involve in detection,
characterization, distillation and quantification
of entanglements associated in various quantum systems.
Nowadays, there are plethora of ideas which pave the way to realize the
more secure and faster information processing tools as well as the
more stable and efficient quantum communication networks.
These technological innovations include cryptography \cite{Ekert},
dense coding \cite{Bennett1}, teleportation \cite{Bennett2} and many more.
Interacting spin models consist of both small clusters and long chains
where the spins are interacting through the exchange
interactions can serve as the platforms to verify the outcome
of those proposals \cite{QSTNE}.
Thermal stability of the entangled state,
on the other hand,
is the main concern to make those protocols operational at room temperature.

Besides those achievements, quantum correlations exhibit dramatic
changes in their values when the system undergoes a quantum phase
transition (QPT) \cite{Sachdev,Somma,JVidal,Wu}.
Again, value of those correlations can be obtained exactly for the spin
models as well as the locations of QPTs can be identified more precisely.
In addition, real materials are also available those could serve as the macroscopic
realizations of any specific spin models.
One of the example of such material is polyoxovanadate compound,
(NHEt)$_3$ [V$_8^{\rm IV}$V$_4^{\rm V}$As$_8$O$_{40}$(H$_2$O)]$\cdot$H$_2$O \cite{Procissi}.
The magnetic properties of this compound are faithfully explained by considering
a four-spin cluster, in which four spin-1/2 degrees are arranged on
the vertices of a square and they are interacting with the nearest one with
isotropic antiferromagnetic (AFM) Heisenberg exchange couplings.
QPT occurs at a definite point for this model in the presence of
diagonal exchange interaction \cite{Bose}.
Experimental evidence suggests that
entanglement can affect the macroscopic properties of solids.
The observed values of specific heat and magnetic susceptibility
for the compound LiHO$_x$Y$_{1-x}$F$_4$ predict that those can be explained
if entanglement of the relevant quantum states are considered explicitly \cite{Ghosh}.
Thermodynamic observables of macroscopic system, like
internal energy \cite{Dowling}, susceptibility \cite{Wiesniak} and
structure factor \cite{Krammer} serve as the entanglement witness (EW),
since the measurement of those quantities eventually leads to the detection of
entanglement. For example, the magnetic structure of deuterated copper nitrate
Cu(NO$_3$)$_2$2.5D$_2$O has been considered as composed of
uncoupled spin-1/2 bond alternating AFM Heisenberg chains
and for this material susceptibility acts as EW \cite{Brukner}.
A rigorous study of entanglement properties for
Heisenberg spin chains in the thermodynamic limit
is a theoretical challenge since the eigenvalues and eigenfunctions are not known
exactly in every case. In many cases, exact results are
obtainable whenever the spin chain is mapped onto a spinless
fermionic models \cite{Korepin,Mezzadri,Osborne,GVidal,Damski}.
Bipartite and multipartite entanglement properties of various
spin models have been investigated at finite temperatures
\cite{Wooters_prl80,Wooters_pra63,Bruss,Glaser,Osterloh,Bose}.
But the analytic derivations of all
entanglement properties for an isolated cluster containing
few spins is possible so far as it is exactly diagonalizable.
Moreover, spin cluster with higher values of exchange
strength can enhance the stability of entangled state at room temperature which is facing a
real challenge nowadays. A spin-cluster material,
copper carboxylate \{Cu$_2$(O$_2$CH)$_4$\}\{Cu(O$_2$CH)$_2$(2-methylpyridine)$_2$\}
is found recently which supports entanglement above room temperature \cite{Souza}.

In this article, a cluster of six spins with all-to-all
two-spin AFM exchange interactions is
considered which gives rise to quantum states with multipartite entanglement
those can withstand thermal agitations.
The model has been solved exactly to obtain all analytic expressions of
eigenvalues and eigenfunctions.
Symmetry of each eigenstate is studied by exploiting the six-fold
rotational invariance of the Hamiltonian.
Bipartite entanglements have been characterized with the help of
concurrence (CN) while the multipartite entanglements are studied by
introducing
several EWs.
The model Hamiltonian is introduced in the Sec. \ref{model}
along with the characterization of frustration embedded in it.
The properties of thermal CN
have been discussed in the section \ref{TC}.
Detection of bipartite and multipartite entanglements in terms of
EWs based on susceptibility, fidelity and internal energy
is presented in the Sec. \ref{ews} while Sec.
\ref{discussion} holds a comprehensive discussion on the results.
\section{The SPIN-$\frac{1}{2}$ AFM $J_1$-$J_2$-$J_3$ HEISENBERG HEXAGON}
\label{model}
Spin-$\frac{1}{2}$ AFM Heisenberg Hamiltonian on the
hexagonal cluster is defined by
\begin{eqnarray}
 H&=&H_{\rm NF}+H_{\rm F},  \label{ham} \\
H_{\rm NF}&=&J_1 \sum_{i=1}^6 \vec S_i \cdot \vec S_{i+1}
+J_3\sum_{i=1,2,3}\vec S_i\cdot \vec S_{i+3},\nonumber\\
H_{\rm F}&=&J_2  \sum_{i=1}^6 \vec S_i \cdot \vec S_{i+2}, \;
\vec S_{i+6}=\vec S_{i}.\nonumber
\end{eqnarray}
$\vec S_i$ is the spin-1/2 operator at the position $i$.
In this model, every spin is interacting with all other spins
via the AFM exchange interactions.
As a result, three topologically different exchange couplings, say,
nearest neighbor (NN), next nearest neighbor
(NNN) and further neighbor (FN) or diagonal exchanges appear
whose strengths are $J_1$, $J_2$ and $J_3$, respectively.
Geometrical view of this spin model is shown in the Fig. \ref{fmodel}(a).
Frustration appears in a magnetic system when all the AFM bonds
are not energetically minimized in the classical ground state simultaneously.
In this model, $J_2$ is frustrating, while
$J_1$ and $J_3$ are non-frustrating.
With this view, the total Hamiltonian, $H$, (Eq. \ref{ham}) is decomposed into
two parts, non-frustrated ($H_{\rm NF}$) and frustrated ($H_{\rm F}$).
Frustration does not appear in this system if $J_2$ is assumed
negative (ferromagnetic).
For $J_2< (J_1 + J_3/2)$,
the classical ground state of this model is a doublet, where each state
is connected to other by flipping the spins in every site.
One of such state, $|\mathcal{G}\rangle$, is shown in the Fig. \ref{fmodel}(c),
in which the adjacent spins are antiparallel.
In this case, energy minimization for both $H_{\rm NF}$ and $H_{\rm F}$ cannot be taken
place simultaneously in the ground state.
Energy minimization of an AFM bond occurs when the spin alignments around this bond
is antiparallel. As a result, energy corresponding to $H_{\rm NF}$ with respect to
the ground state $|\mathcal G\rangle$ is minimized but
that of $H_{\rm F}$ is maximized with respect to
the same $|\mathcal G\rangle$. The frustration of this model can be
characterized by using the quantity, frustration degree ($\mathcal F$)
which is defined as \cite{Sen},
\begin{equation}
\mathcal F={\rm avg}\frac{\langle \mathcal G |H_{\rm F}|\mathcal G\rangle}
{|\langle \mathcal G|H_{\rm NF}|\mathcal G \rangle|},
\end{equation}
where ``avg'' denotes the averaging over all possible ground states.
In this model, $\mathcal F=J_2/(J_1+J_3/2)$.
For the frustrated system  $\mathcal F>0$, while it
is non-frustrated when $\mathcal F\leq 0$.
The higher value of $\mathcal F$ corresponds to the stronger frustration.
The variation of  $\mathcal F$ in the $J_2$-$J_3$ parameter space
is shown in the Fig. \ref{fourplot1} (a).
$\mathcal F$ is found to increase (decrease) with the increase of $J_2$ ($J_3$).
The maximum value of
$\mathcal F$ is unity which appears at the point $J_3=0$ over the line $J_2=J_1$ in
the parameter space.
This particular point is labeled by the letter M in the
parameter space (Fig. \ref{fmodel} (d)).
Therefore, the system is maximally frustrated at the point M.
On the other hand, the minimum value of $\mathcal F$ is zero for this AFM model
which is observed
over the line $J_2=0$, where the system is said to be non-frustrated.
Thus, effects of magnetic frustration on the entanglement properties
can be studied with this model.
\begin{figure}[h]
\begin{center}
\psfrag{1}{$\vec S_1$}
\psfrag{2}{$\vec S_2$}
\psfrag{3}{$\vec S_3$}
\psfrag{4}{$\vec S_4$}
\psfrag{5}{$\vec S_5$}
\psfrag{6}{$\vec S_6$}
\psfrag{J1}{$J_1$}
\psfrag{J2}{$J_2$}
\psfrag{J3}{$J_3$}
\psfrag{A}{(a)}
\psfrag{B}{(b)}
\psfrag{C}{(c)}
\psfrag{D}{(d)}
\psfrag{E}{(e)}
\psfrag{ps1}{$\Psi_{\rm RVB}$}
\psfrag{ps2}{$\Psi_{\rm RVB}'$}
\psfrag{i}{$i$}
\psfrag{e}{$\equiv$}
\psfrag{f}{$\frac{1}{\sqrt 2}$}
\psfrag{b}{$($}
\psfrag{a}{$)$}
\psfrag{u}{$\uparrow$}
\psfrag{d}{$\downarrow$}
\psfrag{m}{$-$}
\psfrag{j}{$j$}
\psfrag{t}{$\sqrt{\frac{2}{3}}$}
\psfrag{p}{$\frac{2}{\sqrt{3}}$}
\psfrag{al}{$\frac{1}{\alpha^\prime_5}$}
\psfrag{c}{$C^\prime_{51}$}
\psfrag{o}{$+$}
\psfrag{,}{,}
\psfrag{M}{\text{\scriptsize{M}}}
\psfrag{P}{\text{\scriptsize{P}}}
\psfrag{g}{$|\mathcal G\rangle$}
\psfrag{L}{\text{\scriptsize{L}}}
\psfrag{cc}{\text{\scriptsize{C}}}
\psfrag{O}{\text{\scriptsize{O}}}
\psfrag{0.0}{\text{\scriptsize{0.0}}}
\psfrag{1.0}{\text{\scriptsize{1.0}}}
\psfrag{0.5}{\text{\scriptsize{0.5}}}
\psfrag{r1}{\text{\scriptsize{R$_1$}}}
\psfrag{r2}{\text{\scriptsize{R$_2$}}}
\psfrag{j3}{\text{\scriptsize{ $J_3/J_1$}}}
\psfrag{j2}{\text{\scriptsize{ $J_2/J_1$}}}
  \includegraphics[scale=0.37]{model_EPJD_corrected.eps}
  \caption{(a) Geometrical view of the model, (b) rotation by $60^\circ$ keeps the system invariant,
(c) classical ground state $|\mathcal G\rangle$, (d) the $J_2$-$J_3$ parameter space
and (e) quantum ground states, $\Psi_{\rm RVB}$ and $\Psi_{\rm RVB}'$.
Expressions of $\alpha^\prime_5$ and $C^\prime_{51}$ are shown in the Appendix \ref{eigensystem}.}
  \label{fmodel}
\end{center}
\end{figure}
The Hamiltonian, Eq. \ref{ham}, commutes with total spin operator, $S_{\rm T}$,
as well as the $z$-component of the total spin, $S^z_{\rm T}$.
 As a result, the Hamiltonian may be spanned in the
different subspaces of $S^z_{\rm T}$ to obtain analytic expressions of eigenvalues and
eigenfunctions.
The exact analytic expressions of all 64
eigenstates ($\Psi_n,\;n=1,2,3,\cdots, 64$) and corresponding energy eigenvalues ($E_n$)
are available in the Appendix \ref{eigensystem}.
Those states essentially comprise to five singlets
($S_{\rm T}=0$), nine triplets ($S_{\rm T}=1$),
five quintets ($S_{\rm T}=2$) and one septet ($S_{\rm T}=3$).
Five distinct singlets are denoted by the eigenstates $\Psi_{38}$, $\Psi_{39}$,
$\Psi_{40}$, $\Psi_{41}$ and $\Psi_{42}$ in the Appendix \ref{eigensystem}.
Among the five, two singlets, $\Psi_{42}$ and $\Psi_{38}$ can be expressed
by two distinct combinations of
dimer states which are known as resonating valence bond (RVB) states.
Those two particular singlets are defined by $\Psi_{\rm RVB}$ and
$\Psi_{\rm RVB}'$.
The arrangements of dimer states in $\Psi_{\rm RVB}$ ($\Psi_{42}$) and
$\Psi_{\rm RVB}'$ ($\Psi_{38}$) are shown in the Fig. \ref{fmodel} (e).
Ground state is always a total spin singlet.
All the five singlets participate in four different manners
to constitute the ground state in the whole parameter space.
Thus, depending on the combinations of singlets in the ground states,
$J_2$-$J_3$ parameter space is decomposed into four segments.
$\Psi_{\rm RVB}$ and
$\Psi_{\rm RVB}'$ are the ground states (non-degenerate) in the regions,
R$_1$ ($J_1+J_3>2J_2$) and
R$_2$ ($J_1+J_3<2J_2$), respectively. $\Psi_{\rm RVB}$ and
$\Psi_{\rm RVB}'$ form the doubly degenerate ground state over the line, L
($J_1+ J_3 = 2 J_2$), junction of the two regions, R$_1$ and R$_2$.
And all the five singlets constitute the ground state
(five-fold  degenerate) at the point P ($J_1= J_3 = J_2$).
Positions of R$_1$, R$_2$, L and P on the parameter
space are shown in the Fig. \ref{fmodel} (d). The area of R$_1$
is three times larger than that of R$_2$.
A first order QPT occurs
across the line L as well as at the point P,
where the ground state cross over takes place.

In addition, the Hamiltonian possesses another useful symmetry,
where it is invariant under the rotation by
$60^\circ$, (Fig. \ref{fmodel}(b)).
For the counter clockwise rotation by $60^\circ$,
a rotational operator, $\hat{R}$, can be defined as
$\hat{R}\bra {S_1S_2S_3S_4S_5S_6}=\bra{S_2S_3S_4S_5S_6S_1}$, where
$\bra{S_1S_2S_3S_4S_5S_6}=\bra{S_1^z}\otimes\bra{S_2^z}\otimes\bra{S_3^z}
\otimes\bra{S_4^z}\otimes\bra{S_5^z}\otimes\bra{S_6^z}$, in which
$\bra{S_i^z}$ is the spin state at site $i$.
So, $\hat{R}^{(n)}$ be the successive $\hat{R}$ operation by
$n$ times, such that $\hat{R}^{(6)}$ is the identity
operation which leaves any state
unchanged. Each eigenstate ($\Psi$) of the Hamiltonian
has some definite rotational property,
which can be characterized in terms of an eigenvalue equation, like
$\hat{R}^{(n)}|\Psi\rangle=\lambda_r|\Psi\rangle$, where
$\lambda_r$'s are the eigenvalues of the rotational operator $\hat{R}^{(n)}$.
$\lambda_r$ can assume the value either $+1$ or $-1$
for the minimum number ($p$) of
 $\hat{R}$ operations on a definite state.
Obviously, for the same state $\lambda_r$ is always $+1$ for $2p$ number of
 $\hat{R}$ operations.
The states with $\lambda_r=+1$ for $p$ number of
 $\hat{R}$ operations have even parity (symmetric)
while those with $\lambda_r=-1$ have odd parity (antisymmetric).
It is found that, every eigenstate has definite values
of both $p$ and $\lambda_r$, and thus has definite parity.
36 states have even parity while the remaining 28 states have odd parity.
Values of $p$ and $\lambda_r$ for all eigenstates are shown
in the Tab. I. It is observed that
$p$ takes up  either 1 or 3 and never
takes up 2, 4 and 5.  For $\Psi_{\rm RVB}$, $\lambda_r=-1$ and $p=1$, while,
for $\Psi_{\rm RVB}'$, $\lambda_r=1$ and $p=1$. Thus,
$\Psi_{\rm RVB}'$ does not change sign
under any number of $\hat{R}$ operations, while $\Psi_{\rm RVB}$ changes sign
for odd numbers of $\hat{R}$ operations. So, $\Psi_{\rm RVB}$ is
antisymmetric, whereas, $\Psi_{\rm RVB}'$ is symmetric under the rotation by
$60^\circ$.
\section{Thermal Concurrence}
\label{TC}
For the Heisenberg hexagon, thermal state density matrix has been written down as
\begin{equation}
\rho(T)=\frac{1}{Z}\sum\limits_{n=1}^{64}e^{-\beta E_n}\rho^n;\quad \rho^n=\bra{\Psi_n}\ket{\Psi_n},
\end{equation}
 where $Z$ is the partition function of the system.
$\beta^{-1}=k_{\rm B}T$, where $k_{\rm B}$ and $T$ are the
Boltzmann constant and temperature, respectively.
Eigenvalues, $E_n$ and the corresponding eigenstates, $\Psi_n$ are
shown in the Appendix \ref{eigensystem}.
Similarly, the reduced thermal state density matrix $\rho_{ij}(T)$
can be written as,
\begin{equation}
\rho_{ij}(T)=\frac{1}{Z}\sum\limits_{n=1}^{64}e^{-\beta E_n}\rho_{ij}^n,
\end{equation}
where the reduced density matrix, $\rho_{ij}^n$ is obtained
from $\rho^n$  by tracing out
the remaining four spin degrees of freedom, those are
not located at the sites $i$ and $j$.
CN is one of the simplest measure to quantify the entanglement
between two qubits when they sit at two different sites in the surrounding of
other interacting spins and that can be derived from the
expression of $\rho_{ij}(T)$.
At $T=0$, $\rho_{ij}(T)$ reduces to $\rho^{\rm G}_{ij}$, where
$\rho^{\rm G}=\bra{\Psi_{\rm G}}\ket{\Psi_{\rm G}}$ and $\Psi_{\rm G}$
is the ground state. $\Psi_{\rm G}$ becomes equal to
$\Psi_{42}$ and $\Psi_{38}$ for the regions R$_1$ and R$_2$, respectively.
On the line L, $\rho^{\rm G}=(\bra{\Psi_{38}}\ket{\Psi_{38}}+\bra{\Psi_{42}}\ket{\Psi_{42}})/2$.
Similarly, at P $\rho^{\rm G}=(\bra{\Psi_{38}}\ket{\Psi_{38}}+\bra{\Psi_{39}}\ket{\Psi_{39}}+
\bra{\Psi_{40}}\ket{\Psi_{40}}+\bra{\Psi_{41}}\ket{\Psi_{41}}+\bra{\Psi_{42}}\ket{\Psi_{42}} )/5$.
Depending on the
positions of the sites $i$ and $j$, only three
different types of  $\rho^{\rm G}_{ij}$ can be constructed.
They are $\rho^{\rm G}_{\rm NN}$, $\rho^{\rm G}_{\rm NNN}$ and $\rho^{\rm G}_{\rm FN}$,
when the sites  $i$ and $j$ are NN, NNN and FN, respectively.
For example, there is six distinct pairs of
NN sites for different values of
$i$ and $j$ (\{$ij$\}), say, \{12\}, \{23\}, \{34\}, \{45\}, \{56\} and \{61\}.
$\rho^{\rm G}_{ij}$ is same for all these six NN pairs by virtue
of the rotational symmetry of hexagon. So, they
are abbreviated as $\rho^{\rm G}_{\rm NN}$.
The similar argument holds true for other combinations, NNN and FN.
NNN corresponds to six distinct pairs while FN corresponds to only three pairs.
The general form of two-qubit $\rho^{\rm G}_{ij}$ in the space of $S^z$ diagonal basis states,
$\{\bra{\uparrow \uparrow},\,\bra{\uparrow \downarrow} ,\,
 \bra{\downarrow\uparrow},\,\bra{\downarrow\downarrow}\}$, looks like,
  \begin{eqnarray}
  \rho^{\rm G}_{ij}=
\left[
 { \begin{array}{cccc}
  a & 0 & 0 & f \\
  0 & b_1 & z & 0 \\
  0 & z^* & b_2 & 0 \\
  f^* & 0 & 0 & d
  \end{array}}
\right].
\label{rho}
\end{eqnarray}
By expressing  $\rho^{\rm G}_{ij}$ in this form
one can define the spin reversed reduced density matrix as,
$\overline{\rho^{\rm G}_{ij}}=(\sigma_y\otimes\sigma_y)(\rho^{\rm G})^{{}^*}_{ij}
(\sigma_y\otimes\sigma_y)$,
where $\sigma_y$ is the Pauli matrix. Then concurrence between the sites
$i$ and $j$ (CN$_{ij}$) is given by
CN$_{ij}={\rm max}\{\lambda_1-\lambda_2-\lambda_3-\lambda_4,0\}$,
where $\lambda_i$s are the square roots of the eigenvalues of the non-Hermitian matrix
$\rho^{\rm G}_{ij}\,\overline{\rho^{\rm G}_{ij}}$, in descending order \cite{Wooters_prl80}.
Since $S^z_{\rm T}$ is the good quantum number,
the element $f$  in $\rho^{\rm G}_{ij}$ (Eq. \ref{rho}) vanishes.
As a result, the expression of concurrence looks simpler, which
is given by \cite{Wooters_pra63}
\begin{eqnarray}
 \textrm{CN}_{ij}=2 \;\textrm{max}\left(0,|z|-\sqrt{ad}\right).
 \label{cn}
 \end{eqnarray}
CN$_{ij}$ measures the pairwise entanglement between two spins at sites $i$ and $j$,
which varies from CN$_{ij}=0$ for a separable state to
CN$_{ij}=1$ for a maximally entangled state.
Variations of CN$_{\rm NN}$ and CN$_{\rm FN}$ for four different
locations in the parameter space are shown in Fig. \ref{fourplot1} (b) and (c), respectively.
CN$_{\rm NNN}$ is zero everywhere which means that
 concurrence between NNN sites does not survive.
CN$_{\rm NN}$ is found to obey the relation CN$_{\rm NN}=-\frac{1}{2}[4E_{\rm G}/N+1]$,
for $J_2=J_3=0$ where $E_{\rm G}$ is the ground state energy of
$S=\frac{1}{2}$ AFM Heisenberg chain with $N$ sites and periodic boundary
condition \cite{Wooters_pra63}. Similar types of relations for CN$_{\rm NNN}$ and
CN$_{\rm FN}$ are not found. CN$_{\rm NN}=0.434$ over the line $J_2=J_3$
which is also maximum. This particular line
is marked by the dashed line OP
in the parameter space (Fig. \ref{fmodel} (d)). CN$_{\rm NN}$ vanishes in the
region R$_2$.
CN$_{\rm NN}$ suffers a jump over the line L,
which is the signature of a first-order QPT.
In R$_1$, for fixed value of the frustrating bond ($J_2$),
CN$_{\rm NN}$ increases with $J_3$
up to the line OP, where it acquires the maximum value.
With further increase of $J_3$, it begins to decrease.
On the other hand,
CN$_{\rm FN}$ is zero throughout the region R$_2$ in addition to the
portion of R$_1$ where  $J_3\leq(0.87J_2+0.14)$.
In the region R$_1$, for fixed $J_2$, CN$_{\rm FN}$
increases with the increase of $J_3$ but for fixed $J_3$, it
decreases with increasing $J_2$.
The maximum value of CN$_{\rm FN}$ is observed over the line
$J_3=J_1$ barring the point P.
There is no effect of frustration on
CN$_{\rm FN}$ in the locations R$_2$ and L.
On the other hand, they tend to decrease with the increase of $J_2$ in R$_1$.
\begin{figure}[h]
\begin{center}
\psfrag{M}{\text{\footnotesize{M}}}
\psfrag{P}{\text{\footnotesize{P}}}
\psfrag{F}{\text{\footnotesize{$\mathcal F$}}}
\psfrag{L}{\text{\footnotesize{L}}}
\psfrag{R1}{\text{\footnotesize{R$_1$}}}
\psfrag{R2}{\text{\footnotesize{R$_2$}}}
\psfrag{J3}{\text{\footnotesize{ $J_3/J_1$}}}
\psfrag{J2}{\text{\footnotesize{ $J_2/J_1$}}}
\psfrag{a}{(a)}
\psfrag{b}{(b)}
\psfrag{c}{(c)}
\psfrag{d}{(d)}
\psfrag{kT}{\text{\footnotesize{$k_{\rm B}T/J_1$}}}
\psfrag{CN2}{\footnotesize CN$_{\rm NN}$}
\psfrag{CN3}{\footnotesize CN$_{\rm FN}$}
\psfrag{CN4}{\footnotesize TCN$_{\rm NN}$}
\includegraphics[scale=1.10]{hexagon_four_plots_1.eps}
\caption{Variations of frustration degree, $\mathcal F$, (a)
 CN$_{\rm NN}$ (b) and CN$_{\rm FN}$ (c) with respect to $J_2/J_1$ and $J_3/J_1$.
(d) Variation of TCN$_{\rm NN}$ with respect to $J_2/J_1$
and $k_{\rm B}T/J_1$ over the line L including the point P.
Orientations of $J_2/J_1$ and $J_3/J_1$ axes are made
different for different figures to have more clarity.}
\label{fourplot1}
\end{center}
\end{figure}

The thermal state concurrence (TCN)
has been derived from $\rho_{ij}(T)$ by using Eqs. (\ref{cn}).
The variations of TCN$_{\rm NN}$ with respect to
$k_{\rm B}T/J_1$ for the line L including the point P has
 been displayed in Fig. \ref{fourplot1} (d).
TCN decreases with temperature  and
exactly vanishes at the critical temperature $T^{ij}_{\rm c}$.
Non-zero values for $T^{\rm NN}_{\rm c}$ and
$T^{\rm FN}_{\rm c}$ have been observed while $T^{\rm NNN}_{\rm c}$
is always zero. Variations of $T^{\rm NN}_{\rm c}$ and
$T^{\rm FN}_{\rm c}$ have been shown in
 Fig. \ref{twoplot} (a) and (b), respectively.
For a fixed $J_3$, both $T^{\rm NN}_{\rm c}$ and $T^{\rm FN}_{\rm c}$ decrease
very fast with $J_2$ whereas for fixed $J_2$, they both increase slowly with $J_3$.
The variations of  both $T^{\rm NN}_{\rm c}$ and  $T^{\rm FN}_{\rm c}$ with respect to
$J_2$ indicate that frustration opposes the bipartite entanglement in this system.
\begin{center}
\begin{figure}[h]
\psfrag{a}{\text{\footnotesize{(a)}}}
\psfrag{b}{\text{\footnotesize{(b)}}}
\psfrag{J2}{\text{\footnotesize{  $J_2/J_1$}}}
\psfrag{J3}{\text{\footnotesize{ $J_3/J_1$}}}
\psfrag{T1}{\text{\footnotesize{$k_{\rm B}T^{\rm NN}_{\rm c}/J_1$}}}
\psfrag{T2}{\text{\footnotesize{$k_{\rm B}T^{\rm FN}_{\rm c}/J_1$}}}
\includegraphics[scale=1.0]{hexagon_two_plots_1.eps}
  \caption{Variation of (a) $k_{\rm B}T^{\rm NN}_{\rm c}/J_1$ and
(b) $k_{\rm B}T^{\rm FN}_{\rm c}/J_1$ with respect to $J_2/J_1$ and  $J_3/J_1$.}
\label{twoplot}
\end{figure}
 \end{center}

\section{entanglement witnesses: susceptibility, fidelity and internal energy}
\label{ews}
In 1996, Horodecki {\em et. al.} formulate the necessary and sufficient
conditions for separability of a bipartite system \cite{Horodeckis}. This formulation leads to
the existence of a particular EW which is essentially a measure of violation of Bell
inequality \cite{Terhal}.
For a magnetic system, it has been shown that magnetic susceptibility can serve
as an EW which can be applied without complete knowledge of the Hamiltonian \cite{Wiesniak}.
 For an isolated  $N$-spin cluster, which is SU(2) invariant and translationally symmetric,
the condition of untangled states has been put forward in
term of an inequality \cite{Brukner}.
For the Heisenberg Hamiltonian, which is isotropic in the spin space,
the magnetic susceptibility along a particular direction, $\alpha$, ($\alpha=x,y,z$) is given by
 \[\chi_{\alpha}=\frac{\left(g\mu_{\rm B}\right)^2}{k_{\rm B}T}
\left(\langle M^2_\alpha\rangle-\langle M_\alpha\rangle ^2\right),\]
 where $M_\alpha=\sum\limits_{i=1}^{N} S^i_\alpha$ is the magnetization along the
direction $\alpha$,
 $g$ is the g-factor and $\mu_B$ is the Bohr magneton. Thus,
 \[\chi_\alpha=\frac{\left(g\mu_{\rm B}\right)^2}{k_{\rm B}T}
\left(\sum\limits_{i,j=1}^{N}\langle S^i_\alpha S^j_\alpha\rangle-
 \langle\sum\limits_{i=1}^{N} S^i_\alpha\rangle^2\right).\]
 Since the Hamiltonian is isotropic in the spin space,
 $\chi=\chi_x=\chi_y=\chi_z$, or,
 $\chi=\frac{1}{3}\left(\chi_x+\chi_y+\chi_z\right)$, and
$\langle\sum\limits_{i=1}^{N} S^i_\alpha\rangle=0$, $\chi$ can be expressed as
 \begin{eqnarray}
  \chi=\frac{\left(g\mu_{\rm B}\right)^2}{k_{\rm B}T}
\left(\frac{N}{4}+\frac{2}{3}\sum\limits_{i<j}\langle \vec S_i. \vec S_j\rangle\right).
\label{chi}
 \end{eqnarray}
The second term in the expression of $\chi$, {\em i. e.},
the sum within the expectation value in Eq. \ref{chi},
acts as the all-to-all spin interaction term.
Alternately, in this particular case, this sum is equivalent to the
Hamiltonian (Eq. \ref{ham}), at the point P when $J_1=1$, say, $H_{\rm P}$. As a result,
$\sum\limits_{i<j}\langle \vec S_i. \vec S_j\rangle=\langle H_{\rm P}\rangle$
corresponds to the ground state energy at the point P for $J_1=1$.
Due to AFM spin interaction the ground state expectation value of
$H_{\rm P}$ is always negative. So, $\langle H_{\rm P}\rangle$
makes a negative contribution to $\chi$.
And the maximum negative value of $\langle H_{\rm P}\rangle$
is equal to the ground state energy of $H_{\rm P}$ itself.
It has been discussed in the next section that minimum energy of the
separable states is negative and equivalent to the ground-state
energy of the corresponding classical Hamiltonian.
For $N=6$, $\langle H_{\rm P}\rangle=-3/4$.
For any general separable states,  $\langle H_{\rm P}\rangle$ always make
lesser contribution to $\chi$ in comparison to
the  separable state of minimum energy.
Therefore, for a single cluster of $N=6$ spin the condition
of untangled states has been given
 by the inequality
  \begin{eqnarray}
  \chi\geq\frac{(g\mu_B)^2}{k_BT}.
  \label{eq}
 \end{eqnarray}
Curves describing the variation of $\chi/(g^2\mu^2_{\rm B}J_1)$ against $k_{\rm B}T/J_1$
arising from the above equality, Eq. \ref{eq} and the same variation resulting
from  Eq. \ref{chi} intersect at a critical temperature, $T_{\rm c}$, below
which the system is entangled. Thus, $\chi$, (Eq. \ref{chi}) acts as an EW.
The variations of $\chi/(g^2\mu^2_{\rm B}J_1)$ against $k_{\rm B}T/J_1$
representing  Eqs. \ref{chi} and \ref{eq} have been
shown in Fig. \ref{t1cx} (a).
Eq. \ref{chi} has been evaluated for $N=6$ where only NN
interactions are considered.
Two curves intersects at $T_{\rm c}\approx 1.43J_1/K_B$.
The variation of TCN$_{\rm NN}$ with respect to $k_{\rm B}T/J_1$
has been shown in Fig. \ref{t1cx} (b), where only NN interactions are considered.
This variation indicates that $T_{\rm c}^{\rm NN}\approx 0.802 J_1/k_{\rm B}$,
where $T_{\rm c}^{\rm NN}$ is that critical temperature beyond which the
bipartite entanglement does not exist.
By comparing the values of $T_{\rm c}$ and $T_{\rm c}^{\rm NN}$,
it is obvious that only multipartite entanglement is present
in the system in the intermediate temperature range $T_{\rm c}^{\rm NN}<T<T_{\rm c}$.
Thus, below $T_{\rm c}^{\rm NN}$, both bipartite and multipartite entanglements are
present while they vanish above $T_{\rm c}$.
The variation of $k_{\rm B}T_{\rm c}/J_1$ for the AFM
Heisenberg hexagon has been shown in Fig. \ref{fourplot2} (a).
$T_{\rm c}$ has the maximum value at the point P when
$J_1=J_2=J_3$, {\em i. e.}, where all-to-all interactions of equal strength are present.
The minimum value of $T_{\rm c}$ appears when $J_2=J_3=0$,
{\em i. e.}, where only NN interactions are present.
With the increase of both $J_2$ and $J_3$, $T_{\rm c}$ increases steadily.
But the rate of increase of $T_{\rm c}$ with respect to $J_2$
is more than that of $J_3$, which means that
frustration enhances the multipartite entanglement in the system.

 \begin{figure}[h]
\psfrag{T}{$k_{\rm B}T/J_1$}
\psfrag{F} {$F$}
\psfrag{cn} {TCN$_{\rm NN}$}
\psfrag{a}{(a)}
\psfrag{b}{(b)}
\psfrag{x2}{Eq.\ref{eq}}
\psfrag{x1}{Eq.\ref{chi}}
\psfrag{t1}{$T_{\rm c}\approx 1.43J_1/K_B$}
\psfrag{t2}{$T_{\rm c}^{\rm NN}\approx 0.80 J_1/k_{\rm B}$}
\psfrag{chi}{$\chi/(g^2\mu^2_{\rm B}/J_1)$}
\psfrag{fidelity}{TCN$_{\rm NN}$, $F$}
\centerline{\includegraphics[scale=0.60]{chi-fidelity_new.eps}}
  \caption{(a) Variations of $\chi/(g^2\mu^2_{\rm B}/J_1)$ against  $k_{\rm B}T/J_1$ following
the Eqs. \ref{chi} and \ref{eq}.
(b) Variation of TCN$_{\rm NN}$ and $F$ against $k_{\rm B}T/J_1$. }
\label{t1cx}
\end{figure}

\begin{figure}[h]
\begin{center}
\psfrag{M}{\text{\footnotesize{M}}}
\psfrag{P}{\text{\footnotesize{P}}}
\psfrag{F}{\text{\footnotesize{$\mathcal F$}}}
\psfrag{L}{\text{\footnotesize{L}}}
\psfrag{R1}{\text{\footnotesize{R$_1$}}}
\psfrag{R2}{\text{\footnotesize{R$_2$}}}
\psfrag{J3}{\text{\footnotesize{ $J_3/J_1$}}}
\psfrag{J2}{\text{\footnotesize{ $J_2/J_1$}}}
\psfrag{a}{(a)}
\psfrag{b}{(b)}
\psfrag{c}{(c)}
\psfrag{d}{(d)}
\psfrag{Esep}{\footnotesize{$E_{\rm sep}/J_1$}}
\psfrag{EGTs}{\text{\tiny{ $k_{\rm B}T_E/J_1$}}}
\psfrag{F}{\footnotesize {$F$}}
\psfrag{kT}{\text{\footnotesize{$k_{\rm B}T/J_1$}}}
\psfrag{CN3}{\footnotesize CN$_{\rm FN}$}
\psfrag{CN4}{\footnotesize TCN$_{\rm NN}$}
\psfrag{T1}{\footnotesize{$k_{\rm B}T_{\rm c}/J_1$}}
\psfrag{EGT}{\footnotesize {$k_{\rm B}T_{\rm E}/J_1$}}
\includegraphics[scale=1.10]{hexagon_four_plots_2.eps}
\caption{Variation of $k_{\rm B}T_{\rm c}/J_1$ (a), $F$ (b),
  $E_{\rm sep}/J_1$ (c) and  $k_{\rm B}T_{\rm E}/J_1$ (d)
with respect to $J_2/J_1$ and $J_3/J_1$.}
\label{fourplot2}
\end{center}
\end{figure}

In order to investigate the presence of six-qubit entanglement in the
AFM Heisenberg hexagon, the state preparation fidelity, $F$ is
defined as, $ F(\rho)=\ket{\Psi_{GHZ}}\rho(T)\bra{\Psi_{GHZ}}$,
 where $\bra{\Psi_{GHZ}}=\frac{1}{\sqrt{2}}\left(\bra{\uparrow\downarrow
\uparrow\downarrow\uparrow\downarrow}
 -\bra{\downarrow\uparrow\downarrow\uparrow\downarrow\uparrow}\right)$
is the six-spin Greenberger-Horne-Zeilinger (GHZ) state \cite{Wang}.
The sufficient condition for the presence of six-particle entanglement
in this six-qubit system is given by the inequality,
$ F(\rho)>\frac{1}{2}$ \cite{Sackett,Bennett}.
For the hexagonal system with $J_2=J_3=0$, variation of $F(\rho)$ against
$k_{\rm B}T/J_1$ has been shown in Fig. \ref{t1cx} (b).
The variation of ground state fidelity $F$ in the
parameter space is shown in Fig. \ref{fourplot2} (b). The value of $F$
is fixed over the line OP and that value of $F$ is $0.458$.
The maximum value of $F$ at zero temperature is $1/2$ which is observed
over another line  $J_3=J_1$ except the point P.
$F$, however, vanishes over the entire region R$_2$.
The value of $F$ just over the line L is fixed, and it
suffers a sudden jump, which is the manifestation of QPT.
$F$ decreases with the increase of $T$ throughout the parameter space.
Since $F(\rho)\leq\frac{1}{2}$, the six-spin entanglement is
absent in the ground as well as the thermal states
at all temperatures.
On the other hand, for $S=\frac{1}{2}$ AFM
Heisenberg tetramer with NN interaction, $F=\frac{2}{3}>\frac{1}{2}$,
which indicates the presence of
four-particle entanglement in ground state \cite{Wang,Bose}.
In general,  $F$ increases with $J_3$ for fixed $J_2$ and
decrease with $J_2$ for fixed $J_3$. Therefore, frustration opposes the
six-spin entanglement in this case.

Another kind of detection for EW has been introduced
by Dowling and others based on a comparison between
the internal energy ($U(T)$) at finite temperature, $T$, and
the minimum separable energy ($E_{\rm sep}$) \cite{Dowling}.
The entanglement gap energy, $G_{\rm E}$ is defined by
$G_{\rm E}(T)=E_{\rm sep}-U(T)$, at non-zero
temperature  while that at zero temperature is given by
$G_{\rm E}(0)=E_{\rm sep}-E_{\rm G}$, where $E_{\rm G}$ is the ground state energy.
$U(T)$ is given by $U(T)=-\frac{1}{Z}\frac{\partial Z}{\partial \beta}$.
The multipartite entanglement would be present in the
system at non-zero temperature, whenever $G_{\rm E}(T)>0$.
With the increase of $T$, $G_{\rm E}(T)$ decreases
since $U(T)$ increases with $T$. Obviously, there would be a limiting value
of  $T$ above which $G_{\rm E}(T)<0$.
This critical value of temperature, known as the entanglement
gap temperature ($T_{\rm E}$) is define by, $U(T_{\rm E})=E_{\rm sep}$.
Therefore, below $T_{\rm E}$  multipartite entanglement is non-zero.
Thus a thermal state is entangled if $T<T_{\rm E}$.
To formalize this analysis, an EW, $Z_{\rm EW}$, a Hermitian operator
is introduced such that Tr[$Z_{\rm EW}\rho_{\rm ent}$]$<0$, when
there exists an entangled state, $\rho_{\rm ent}$. It is noted that
$Z_{\rm EW}$ witnesses multipartite entanglement in $\rho_{\rm ent}$.
Therefore, positive entanglement gap, $G_{\rm E}(T)>0$, defines the
EW by the equation $Z_{\rm EW}=H-IE_{\rm sep}$,
where $I$ is the identity matrix on the Hilbert space.
Hence, Tr[$Z_{\rm EW}\rho_{\rm sep}$]$=$Tr[$H\rho_{\rm sep}$]$-E_{\rm sep}\geq 0$, when
 $\rho_{\rm sep}$ is any separable state while $E_{sep}$ is the lowest possible
energy for a separable state. On the other hand, for the ground state,
 $\rho_{\rm G}$, Tr[$Z_{\rm EW}\rho_{\rm G}$]$=E_{\rm G}-E_{\rm sep}< 0$ at $T=0$.
Thus, $Z_{\rm EW}$ serves as an EW.

Generally variational methods are being employed to find the
lowest possible energy for a separable state of spin chains.
Otherwise, it has been noted that for AFM Heisenberg spin cluster
with all-to-all couplings of same strengths,
a minimum energy separable state is given by that classical
spin configuration where the total spin vector is zero \cite{Dowling}.
In order to find the separable state with minimum energy
in this case, we
introduce the most general form of separable state, like,
$|\psi_{\rm sep}\rangle=\prod_j|S_j\rangle$, $j=1,2,3,\cdots, 6$,
where $|S_j\rangle=\cos{\theta_j}|\uparrow\rangle +e^{i\phi_j}
\sin{\theta_j}|\downarrow\rangle$,
$0\leq\theta_j\leq \pi$, and $0\leq\phi_j\leq 2\pi$. $E_{\rm sep}$
is obtained by minimizing $\langle \psi_{\rm sep}|H|\psi_{\rm sep}\rangle$
with respect to both $\theta_j$ and $\phi_j$. By using simplex minimizing
procedure \cite{Nelder_Mead}, $E_{\rm sep}$
is found to equal to $ -\frac{3}{2} (J_1 - J_2) - \frac{3}{4} J_3$,
which essentially corresponds to $\theta_j=\frac{2\pi j}{6}$ and $\phi_j=0$.
The symmetry in the Hamiltonian is responsible for the
symmetric solutions.
The solutions always correspond to the classical spin configuration
with the total spin vector is zero,
although the condition of all-to-all couplings of same strength is
mostly violated except the point P.
The variations of $E_{\rm sep}/J_1$ and $k_{\rm B}T_{\rm E}/J_1$
are shown in Figs. \ref{fourplot2} (c) and (d), respectively.
Usually $E_{\rm sep}$ is negative everywhere except
the extreme point, M, over the line $J_1=J_2$, where $E_{\rm sep}$ becomes zero.
At the point M, the value of frustration degree, $\mathcal F$ is the maximum and
$T_{\rm E}$ tends to $\infty$, which is shown in the Fig. \ref{fourplot2} (d).
The value of $k_{\rm B}T_{\rm c}/J_1$ at this point is 2.395.
The bipartite entanglement vanishes over the same line including this point.
Therefore, at this point multipartite entanglement survives
at all temperatures in the absence of bipartite entanglement.
Besides this particular point, M, entangled states are found to exist at high
temperatures in the vicinity of the point.
Thus, the entanglement in quantum states in this particular region
exhibits a robustness to the thermal noise.
It appears from the expression of $E_{\rm sep}$ that positive contribution
to $E_{\rm sep}$ only comes from the NNN frustrating bond, $J_2$.
So, in the absence of NNN bond, $E_{\rm sep}$ is always negative which gives rise to
very low $T_{\rm E}$. Therefore, the presence of frustration leads
to the high values of $T_{\rm E}$.
This observation shows that the frustration
induces the multipartite entanglement in this spin
cluster in such a manner that it does sustain against the thermal agitation.
On the other extreme point P over the same line $J_1=J_2$,
it is found that $T_{\rm E}=T_{\rm c}= 2.862 J_1/K_{\rm B}$.
Since the bipartite entanglement vanishes over this line
only multipartite entanglement survives in the system at P for $0<T<T_{\rm E}$.
The equality between $T_{\rm E}$ and $T_{\rm c}$ results from the fact that
 at this point the effective spin interactions are defined
on a non-bipartite graph or lattice for which EW based on thermal energy
detects only the multipartite entanglement.
Now consider another point O ($J_2=J_3=0$) in the parameter space,
where $E_{\rm sep}=-1.5J_1$, and the value of
$T_{\rm E}$ is 0.802$J_1/K_{\rm B}$ which is identical to that of $T_{\rm c}^{\rm NN}$.
This is due to the fact that at this point the resulting spin interactions are defined
on a bipartite graph or lattice and EW based on thermal energy in this case
detects only the bipartite entanglement.
\section{Discussion}
\label{discussion}
The spin-$\frac{1}{2}$ AFM Heisenberg hexagon with
all-to-all exchange couplings is considered to
investigate the variety of entanglement properties.
Four different locations, R$_1$, R$_2$, L and P have been identified
where the nature of ground states are different while
QPT occurs over the line L including the point P.
By exploiting its six-fold rotational symmetry three different kinds of
CNs, CN$_{\rm NN}$, CN$_{\rm NNN}$ and CN$_{\rm FN}$ are introduced and those give
totally different results.
Both $T_{\rm c}^{\rm NN}$ and $T_{\rm c}^{\rm FN}$ decrease with
the increase of $J_2$ (Fig. \ref{twoplot}) and ultimately vanish over the lines
$J_2/J_1=1$ and $J_3/J_1=0.87J_2/J_1+0.14$, respectively.
Those observations reveal the fact that the frustration
opposes the bipartite entanglement in this system.
Multipartite entanglements of this model have been studied where susceptibility,
fidelity and internal energy serve as the EWs. Multipartite entanglements survive
up to the temperature, $T_{\rm c}$ which is always higher than the $T_{\rm c}^{\rm NN}$.
Thus, the bipartite entanglement diminishes due to thermal agitation
more quickly than the multipartite entanglement. Frustration leads to the
higher values of $T_{\rm c}$, so it favors the multipartite entanglements.
Fidelity measurement indicates that this model exhibits no six-spin entanglement
even in zero temperature.
Survival of multipartite entanglement at finite temperature
has been studied in terms of internal energy as EW. Entanglement is found to
persist at high temperatures in this system in the vicinity to
the point M,
where value of $\mathcal F$ is the maximum.
It appears that frustration is responsible for the robustness of
quantum entanglement against the thermal effect around this point.
Existence of the multipartite entanglement at finite temperatures
is found in this system where the bipartite entanglement vanishes at non-zero temperatures.
EW in terms of susceptibility can detect the existence of both bipartite and multipartite
entanglements collectively at finite temperatures.
On the other hand, EW in terms of internal energy can
detect bipartite and multipartite entanglements separately for the cases
when the spin interactions are defined
on bipartite and non-bipartite graphs or lattices, respectively.
For this model, EW based on internal energy
detects only the bipartite entanglement at the point O in the parameter space, and
that measures only the multipartite entanglement at the other point P.
Therefore, at the point O,  $T_{\rm c}^{\rm NN}=T_{\rm E}$.
Similarly, $T_{\rm c}$ becomes equal to  $T_{\rm E}$ only at the point P, where
only multipartite entanglement survives and measured separately by the EWs based on
susceptibility and internal energy. It further appears that EW based on
internal energy detects the collective existence of both bipartite
and multipartite entanglements everywhere in the $J_2$-$J_3$ parameter space
except the points O and P. Therefore, development of
more effective EWs is necessary for precise detection of different types of
entanglements separately.
Engineering of entangled quantum state at room temperature is a new challenge.
So, the frustrated AFM spin models could shed light in this direction.

The inelastic neutron scattering study on Cu$_3$WO$_6$
reveals that spin-1/2 Cu$^{2+}$ ions
are arranged on the vertices of
hexagons in its crystalline state \cite{Hase}.
Dynamic structure factor
predicts the magnitudes of $J_1$, $J_2$ and $J_3$
are 78.5K, 50.4K and 40.0K, respectively.
As they satisfy the relation $J_1+J_3>2J_2$, this system belongs to
the region R$_1$ having the RVB ground state, $\Psi_{42}$.
Position of this compound in the $J_2$-$J_3$ parameter
space is identified by the point C.
Estimations of various quantities for
Cu$_3$WO$_6$ yield following values. $\mathcal F=0.51$, CN$_{\rm NN}=0.43$,
$k_{\rm B}T^{\rm NN}_{\rm c}/J_1=0.50$, $F=0.44$, $k_{\rm B}T_{\rm c}/J_1=2.20$,
$E_{\rm sep}/J_1=-0.92$ and  $k_{\rm B}T_{\rm E}/J_1=1.33$.
Hence, this material is no more suitable to yield thermally stable
multipartite entanglement.
Therefore, in our opinion synthesis of new AFM compounds
whose compositions as well as structures are very close to Cu$_3$WO$_6$
or other one
such that $J_2 \geq J_1+J_3 /2$ becomes necessary for the production of
thermally stable multipartite entanglement.
\section{ACKNOWLEDGMENTS}
MD acknowledges the UGC fellowship, no. 524067 (2014), India.
AKG acknowledges a BRNS-sanctioned
research project, no. 37(3)/14/16/2015, India.
\section{Author contribution statement}
MD did the analytical work and AKG did the numerical work.
The manuscript was prepared jointly by both the authors.

redpajama_set_name: RedPajamaArXiv


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For businesses up and down the country, whether a start-up or a longstanding and successful eCommerce store, finding the right marketing strategy for your individual niche and business objectives is essential.
Introducing your products to a new audience or maintaining a well-established and loyal customer base both require a bulletproof marketing plan. This plan must include staying up to date with the new and current marketing trends that could benefit your business and techniques to consider implementing to produce results across different methods of marketing. Marketing strategies for eCommerce businesses like yours centre around a structured website, as this ultimately represents your shop.
This said, it is important to create and launch a website that creates the image of your brand and that offers a user-friendly experience. These are all elements that must be considered before creating and implementing a marketing strategy for your eCommerce store. Without a well-optimised website, your marketing efforts will be sending people to your website which visitors may find hard to navigate and use.
Below we discuss a selection of marketing strategies for eCommerce businesses that if implemented correctly can create results for businesses just like yours, keep reading to learn more.
By creating high-quality content you are more likely to stand out and resonate with your customers in a way that makes them want to interact with your brand, hopefully resulting in a sale and a loyal customer. If your eCommerce store sells as a third party website we recommend that you create your own style of product descriptions as this will allow your product to rank. As if you were to use the same product description that the manufacturer used you would find your brand competing with the manufacturer's website directly.
Content does not simply refer to the written copy on the website, consider the branding that you are using to represent your business. Software like Adobe Photoshop and Canva have meant that re-engineering visual content has become possible within minutes. We recommend that you spend time and money on creating or purchasing original graphics as these will project your brand image in a better way.
A note that we recommend you consider here when creating any content is to be both creative and original.
eCommerce is an incredibly competitive business model, which we know you are all too aware of. However, as consumers have become the MVP of the eCommerce industry, it is more important than ever to stand out in a unique way. Creating an experience for the consumer that they will not forget is more important than ever as the power is in consumers hands. We have the ability to search for anything, product or service, at any time or place, thanks to our friends Google. This illustrates further the importance of staying on top of consumer trends, competitive pricing structures and user experience in order to maintain a loyal customer base.
As a result of this, it is more important than ever to customise their user experience (UX) to cater to the variety of needs of your audience. It is important to create a brand that has a personal appeal, a tone of voice that resonates with your customers and entices them to believe that your store is similar to their own personality.
Make your marketing centre around your customers. Take time to get to know your customers, what they like, what they don't like and what their buyer's journey looks like. Of course, not every customer will have the same characteristics however you may find the common area between particular trends or consumer preferences. The best way to then get this to work in your marketing is to create "Buyer Personas", this allows you to create individual experiences for each Persona type. From here we then recommend adding personal touches like addressing your prospect by name, through whichever medium you are conversing, social media, email, post etc.
Another way to create the more personal approach is when you are promoting your own business consider being transparent about your company processes and procedures. Share genuine photos of your team and employees, almost creating a behind the scenes feel for your audience. This helps create a personality for your business and will hopefully create a face for your eCommerce store and can contribute to a loyal customer base.
This should no longer be considered as a new medium in which you can connect with your potential customers. However, social media has changed the way in which so much is done, from instigating conversations to expressing our concerns with products or service. As an eCommerce business, this can make or break your reputation as it is important to respond to any concerns that your customers may have in regards to delivery or product details. These elements continue from the previous point, in creating relationships with your audience and continuing with a brand personality.
Social media offers unprecedented opportunity to generate engagement and interaction, boost traffic to your website and connect with a larger base of customers. Utilising the different approaches that are available with each different social media platform is essential when deciding which platforms connect with your audience and your product niche. It is important to remember that not every social media platform may be relevant for your business. Social media marketing strategies for eCommerce businesses must continue to create a personality and maintain this personality is essential in order to have a consistent brand. Which in turn will build trust with your audience, changing personality for each post will create doubts for your audience as to your legitimacy. Therefore it is essential that any member of the team who has an input for the social media must understand the company's communication style and stick to that.
Search Engine Optimisation is one of the most important elements for a successful eCommerce website as it is the process of making sure your online store is optimised for search engines. It is a manual task and the benefits are truly worth the work. With the standards of SEO these days, it should be at the top of your marketing hit list, if you are not already working to optimise your website for your users. Your SEO strategy should run alongside your content creation, combining these two elements of your marketing will allow you to reap the benefits of a fresh and informative website.
Your website should answer any questions or concerns that your users may have with your business and the products that you sell. SEO allows you to use keywords in order to understand customer concerns and using these within your content will mean that your website will flag up as a matching result to answer that specific user query.
SEO is not only the representation of your site on search engines, as you could answer the user query, however, your site could then offer a poor user experience and hard to navigate buyer journey. This, in turn, could lose you visitors and damage your brand. Good UX optimisation allows you to ensure that you are providing a smooth flow throughout your website, from Landing Page optimisation to easy to navigate pages.
We discuss these elements and more in our FREE downloadable eBook on Organic vs Paid Search Marketing. If you are unsure whether implementing an SEO or PPC marketing strategy would suit your business objectives, we recommend you download it. Take a read as the ideal combination of the two differs for each business and we hope that it helps illustrate the pros and cons of each strategy.
For each PPC campaign, there are three key elements that must be considered before adding budget to a campaign. These are the ad itself, the offer that the ad is promoting and the landing page that the ad takes the user to.
All three elements must not only work in harmony, be optimised for the user and also maintain the interest of the user that is clicking on the ad. The landing page is the end location for the visitor so it is essential that is a continuation of the ad and is not taking the user to a different location. It must deliver what was promised in the ad itself, in order to take the visitor through your conversion funnel, if the user is not met with what they expected they are likely to leave rather than search for it on your site. Therefore you will have paid for the click but made no gain.
These three elements of a paid campaign must work in synchrony, we discuss how to create a flawless paid campaign and we also compare it to the results that you can expect from creating an organic or paid campaign in our eBook. If you want to know which approach would work better for you, we recommend that you take a read.
We will finish with one element of your marketing strategies for eCommerce businesses that have become one of the most important within the last two years. Mobile. As an eCommerce store more and more consumers are visiting your site on a mobile device. Com Score reported that mobile devices are our primary tool for time spent online, in the UK we spend 61% of our time on a mobile device. With the UK at the lowest percentage, Indonesia surpasses everyone with 91% of time spent on mobile.
This being said, your mobile experience should be as easy to navigate as your desktop, it is essential to make sure the navigation works across multiple platforms, such as mobile, tablet and desktop. Any buttons that are clickable should be made clickable across devices, an element to consider here is making it easy to navigate with fat fingers. As clicking the wrong button or not being able to click any button is just doing to distract from your brand and create a negative user experience.
Also, consider that you are not bombarding the user with pop-ups that take up their full mobile screen or that automatically force and app download. Similar to a paid campaign make sure that your experience is streamlined and allows them to flow through the process, across multiple devices.
Make sure that you are delivering an experience that the user is expecting and it is essential to make the investment in making sure your website is fully responsive regardless of the device that it is being viewed on.
When it comes to effective marketing strategies for eCommerce businesses like yours, it is important to stay up to date and aware of the latest marketing trends, techniques and consumer behaviour. You must find the correct combination of marketing elements for your business and this is even more important when it comes to digital marketing. Hence why we have created this free, easy to understand eBook that puts organic search and paid search head to head to which method you should implement for your business.
Reach out to your consumers in a variety of ways and create a personality rather than simply a corporate appearance. A final thought is, as always, to make sure that you are monitoring, analysing and evaluating your website analytics to examine trends, keep your website optimised and track your results to improve and improve and improve your marketing approaches.


44 Accidentally Vegan Snack Foods – PETA Snack list!
Going vegan doesn't mean completely abandoning the foods you enjoyed before making the transition. Many products on store shelves are unintentionally vegan. Check out some of our favourite "accidentally vegan" snacks.
Note: Please always be sure to double-check the ingredients before purchasing anything on this list, as manufacturers are at liberty to change their ingredients at any time.
Hello again! I've put together this list which I hope you will find useful. Most of the spices I use in my curries are listed here and will cost very little to stock up from an Asian store. Once you are armed with these you will change your mind about cooking curries and contrary to some theories I have heard, it doesn't take a day and more to prepare a delicious curry! An English friend of mine whose parents lived in India during colonial times would swear that her Mum needed at least 2 days to prepare curry and I have never figured how that was possible and she never elucidated. I cook every day and have all my spices handy and a larder stocked with basics which means I don't spend a day in the kitchen stirring a pot! You will see that I use curry powder and tend not to use these spices individually. The reason being that there are some very good curry powder mixes on the market and it cuts cooking time if you find a good one and stick to that. I trust and use Bolst Mild Curry Powder and it serves me very well. People are sometimes surprised when I say I use ready mixed curry powder but the truth is there is no harm and it does the job and makes my life easy, so why not?
As for frying onions and grating garlic and ginger, well that too can be made easy if you are pushed for time. Use ready fried onions (not gluten free, so check) and ready minced garlic and ginger. Some recipes do need freshly fried onions where the onions are a prominent feature of the recipe but for say sag tofu (spinach with tofu) you could use ready fried onions with impunity. Generally speaking, where the recipe requires 1 medium fried onion, use about 2 tablespoons of fried onions.
Here's the list you need to take with you to the Asian store – if in doubt just ask them for help or email me. The links for Bolst curry powder is to the Asian Cookshop and you will find a vast array of spices to tempt you if you prefer to buy online! I've listed most of what comes to mind and each recipe has a slightly different combination of a few, not all!
In my experience, for those who don't do it regularly, cooking rice is a challenge but it needn't be. In Pakistan where I come from people don't cook rice using exact measurements – in fact most people don't use exact measurements for cooking anything other than dishes prepared in huge quantities for special occasions! For everyday cooking women mostly rely on judgment, experience and the 'eye' to measure ingredients. I remember when asking my mother for a recipe she would say put in a 'muthi' (fistful) of this or a 'chutki' (pinch) of that!
I decided to jot down some facts to demystify rice for those who have either never attempted to cook rice or those who have and not got it quite right and never looked back. If you follow some simple rules and learn to use your 'eye', it's as easy as pie.
There are literally thousands of varieties of rice grown around the world but we are going to talk about white long grain rice generally known as Basmati.
When cooking rice which is to be strained you need to use a lot of water to keep the rice grains separate, just as you would for pasta and this is simple.
Rice cooked in stock or a sauce is slightly trickier. This method is used when you add vegetables or stock to the rice and wish to retain the flavours of the stock, for example all pilaus are cooked in stock or sauce.
Boiled or steamed rice is best cooked in a lot of water in a large pan to give the rice room to expand and fluff out.
Pilau rice is not strained but cooked in a stock usually with vegetables or pulses e.g. pilau rice. As a rule of thumb I use 1½ -2 times of water for one measure of rice which has been soaked for 1 hour. There is no exact rule; some people use a little more water and you may find that works for you; much depends on the type of rice you are using and the soaking time – read on!
Generally, pre-soaked good quality Basmati will cook in less than 3 minutes once it has come to the boil. Brown rice takes a lot longer to cook.
In this method, rice is added to vegetables or beans usually in a broth. The broth will have been prepared and some vegetables or beans added. In this case you will already have the liquid in the pan, either by way of stock or a sauce. It is not possible to measure the sauce in the pan with vegetables! Here is where 'eye balling' is useful means of ensuring you don't have too much liquid – if you do, dry it off a bit. We are aiming to get a rough ratio of 1½ times liquid to one portion of rice.
There should be enough liquid to just cover the rice (see picture below). If it looks too dry add a little water so the liquid is skimming the surface of the rice and vegetables – eye ball!
Cooking rice in broth is where people usually come unstuck. If you follow the rule of the 'eye' to judge the level of the water in the saucepan, you will be fine.
When cooking rice in stock it is all about the ratio of liquid to rice. However, we need not panic – it is easily remedied.
If there is too much water, all you need to do is boil it rapidly to reduce the liquid before covering it with the lid to steam. If there isn't enough liquid, simply add a splash of boiling water – keep the kettle on. Boiling water can be added at any stage if required.
Generally, if you don't soak the rice or it isn't the best quality, you will need to use more water. Once you've done this a few times you will sail through it and wonder what the fuss is about.
Below is a picture of rice with broad beans in tomato sauce. I usually use this large wide saucepan for rice with vegetables. As you will see the liquid is skimming the surface – this rice required less water due to the tomato sauce. Bring rapidly to the boil and then steam on lowest heat for 15-20 minutes – can't go wrong!
Rice is a very versatile grain and a staple diet in many parts of the world. It is gluten free and perfect for those who are sensitive to gluten. Pilau rice or rice cooked in stock can be slightly tricky but once you've tried it, you will get the 'feel' for it very quickly. In any event, what is the worst that could happen? It would go a bit soggy maybe? a tad mushy? it would still taste beautiful so why not give it a go.
If you get stuck or have any questions I am happy to help. Let me know how you get on!
I recently read that freezing tofu changes the texture and makes it chewier! Next thing was to have a go which I did and, guess what, it does! So well worth it and here's how…. Get some firm tofu and slice into about ¼ inch slices, drizzle some soy sauce on the tofu and freeze. Only freeze as much as you wish to use for one meal as once defrosted, you need to cook it. To defrost you could either leave it out at room temperature or place the container in warm water. Always remember to squeeze the tofu to remove excess liquid. I find the best way to do this is to place 2 sheets of kitchen paper on the chopping board, place slices of tofu on it and then cover with another 2 sheets of kitchen paper. Press gently with the palm of your hands and the kitchen paper will absorb the moisture. Change the paper if it gets too soggy and squeeze again – always handle tofu gently and with care as it breaks easily. Use this method to remove excess water from tofu even if you don't freeze it. Squeezing in the palms of your hands can be tricky and not efficient – I find placing it in kitchen paper works best. For more information on different types of tofu check this site. This is what I did for these tofu bites and they turned out really chewy and dry which is the result we are looking for in fried tofu! Have a go and leave your comments.
I bought hickory flavoured liquid smoke a while back and recently used it to marinade tofu – it turned out amazing (see recipe for Smoky tofu bites). Was just browsing to find the same online to add to my hints & tips post and found this! Multi-pack of Colgin Liquid Smoke in 4 different flavours.


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New Outdoor Gear Shop Opens in Millcreek With Focus on Community and Sustainability
Lone Pine Gear Exchange offers the outdoor community a place to buy, sell, and repair their gear. The shop also includes a coffee shop, plastic-free refill station, and gathering space for outdoor-focused events.
When it comes to outdoor gear, Lone Pine Gear Exchange aims to be a one-stop-shop for the Salt Lake City outdoor community. The new business just opened in the Millcreek area and offers retail, consignment, ski tuning, gear repair, as well as a plastic-free refill station, coffee shop and gathering space. With the belief that "small acts can make big impacts," Lone Pine seeks to keep outdoor gear in circulation and out of landfills. The gear shop has also committed to plant one tree for every sale made through a partnership with One Tree Planted.
Located at 2835 East 3300 South, the retail space features new and used gear for sports such as skiing, snowboarding, biking, camping, and rafting. Lone Pine offers ski tuning and gear repair via its Wintersteiger Tune Shop, as well as two industrial sewing machines for softgood repairs like zipper replacements, and tears in jackets or tents. The shop will also repurpose irreparable items into things like reusable shopping bags, fanny packs, hydration packs, and down booties.
The Shred Ready coffee bar downstairs pours Salt Lake City Roasting coffee, Townshend Tea, and serves pastries and breakfast burritos by Lone Pine bakery - customers can grab a coffee in the shop or drive through on their way up to the mountain. Lastly, in an effort to reduce single-use plastic, the shop also has a "refill station" where customers can buy everyday products like soap and shampoo by the ounce, or find alternatives for plastic items like produce bags, floss, and toothbrushes.
The husband and wife duo behind Lone Pine, Ben Johnson and Katy Jackson, are no strangers to the outdoor industry. They have owned and managed similar businesses in the past, but both were passionate about creating a community space that truly reflected their values. "Like our customers, we live here because we love the outdoors. We wanted to ensure that we were providing our local community with resources to repair the gear they love, resell items they no longer need, and of course find any new or used items they need for outdoor adventures," said Katy. "We also wanted to make a concrete environmental commitment, so we are thrilled to partner with One Tree Planted."
Lone Pine is also opening its doors to outdoor organizations who may need space to host events. They just hosted their first event earlier this month with the Utah Avalanche Center in partnership with Roha Brewing, and have another event with Steven Clark, an avalanche forecaster for UDOT, scheduled for Friday February 21 at 7:00. "We are really excited to have a space to gather our community," said Ben. "We hope people feel welcome to come and hang out, and that organizations will reach out if they want to utilize the space to further their cause."
Although Lone Pine had a soft opening in January, they plan to make their launch more official this week. There will be a ribbon cutting ceremony with the Millcreek Business Council and Mayor Jeff Silvesstrini on Tuesday, February 18 at 1:30pm. In celebration, the shop will be offering free ski and snowboard tunes for all customers that drop off their gear between 1-2pm that day.
Learn more about Lone Pine Gear Exchange by visiting the website and following them on social media at @LonePineGearX. Events will be listed on Lone Pine's Facebook page.
February 07, 2020 — BoostCommerce Collaborator
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LaTia has 10 years of experience with our Coordination Department, having first started with us in 2008. She has been involved on some level in every aspect of Coordination, and now manages the department. Prior to her time with us, LaTia was a voice teacher and an opera singer, as she holds a Bachelor's Degree in Vocal Performance. You're most likely to hear LaTia's voice on the end of the line when you call our offices, and if you ask nicely, she may sing for you!


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How's the long weekend treating you? Make the most of your bonus day with these must read links. I've been saving them up for months. It's a good batch. Fashion is heavily influenced by functional apparel. Famously, blue jeans morphed from sturdy, miners' gear to the epitome of LA chic. And this sort of style evolution is happening all the time. Check out how a simple length of tube bandage evolved into a ubiquitous NBA accessory. Via the New Yorker.
"I often use mesh and chain mail in my costume designs," he said, "and I was fascinated by the opportunity to make something light and fluid out of rigid materials." A Crystal-Crusted Gown for Dita Von Teese Made with a 3-D Printer
Of the Famous Artworks That Inspired 15 Films, I think The Blue Boy + Django Unchained is my favorite, because fashion history and Quentin Tarantino. But the rest of the list is pretty darn fascinating.
"In a survey of graduating professional students, Linda Babcock, of Carnegie Mellon University, found that only seven per cent of women attempted to negotiate their initial offers, while fifty-seven per cent of the men did so. We see those dire statistics and think that women are, in a sense, self-sabotaging.... But is it really the case that the disadvantage stems from not asking?" Via The New Yorker.
marilyn-monroe-in-bed-pic-613x478
We all know that the genius of Marilyn Monroe was way underestimated during her lifetime. Fortunately, internet scholars are posting her pearls of wisdom for our own edification: "By nature, I suppose I have a languorous disposition. I hate to do things in a hurried, tense atmosphere, and it is virtually impossible for me to spring out of bed in the morning. On Sunday, which is my one day of total leisure, I sometimes take two hours to wake up, luxuriating in every last moment of drowsiness."
The radness that is Mary Kay Chin, one of the founders of SF Yellow Bike and San Francisco Bike Party. Via the Manic Fixie Dream Girls of Chicago's Tiny Crush Blog.
bikiegirlbloomers
A hearty congratulations to Bikie Girl Bloomers on the completion of a successful crowd-funding campaign. That means we can expect more lace-trimmed spandex bloomers in classic colors and fun prints. (I'm a fan of the polka dot pair.)
vintage bike ad
A round-up of gorgeous turn-of-the-last-century vintage cycling ads, via Iladora. I want to live inside every single one.
"Do I have some magical skill set that allows me to ferret out...deals? Nope. Are my methods top secret and difficult to employ? No way. Do I troll eBay on a daily basis looking for deals … well, sort of, but we'll get to that." Sally of Already Pretty breaks it down in the ultimate guide to buying clothes on eBay.
fashion history head wraps and hoodies
"The ladies in the photo exude a sense of dignity, which I believe is a protest in and of itself. Their head wraps simply added to that power. Then I remembered how other articles of clothing have been an important symbol for various protests and revolutions—particularly involving Africans and African Americans—throughout the years." Scripts and Sightings explores where fashion history and social justice meet and mingle.
Paris-Velib-Bike-Pretty-Satchel-Bag-2.jpg.pagespeed.ic.L2Wh5DBzX4
Bike Pretty's very own Kelly and her hunky French boyfriend Seb are leading a tour of the Tour de France: We will leave South London on Friday 25 July, cycle 70k to New Haven, take the overnight ferry to Dieppe. Then cycle 130k on Saturday 26 July where we will end the day camping. On day 3, we will cycle 80k to Paris, where we hope to catch both the women's and men's Tour de France. And you're invited! Sign up via the London Bike Kitchen newsletter.
Beret-et-Baguette-Paris-2013-Street-Style-Photos-Kelly-Miller-0 (1)
Argh, scarves! How can something so simple (just a freaking length of fabric, yeah right) never fail to frustrate the daylights out of me. I usually just ball them up and throw them in the back of my closet. But there is a better way to make them work: How to Tie a Scarf Like a Parisienne, via Vogue.
"I am sick of hearing that only stupid, shallow people buy into the unrealistic expectations society has of women. Because as much as I try to fight it, I often buy into them. Does that make me shallow and stupid? Is it therefore MY FAULT that I feel inadequate sometimes – because if I was more intelligent and not so vain, these expectations wouldn't affect me, would they?" I'm Fed Up of Being Told I'm 'Too Smart' To Fall for Body Fascism
And finally, watch Renee's mini-teaser for her upcoming eBike documentary!
Jul 06, 2014 • Melissa Davies • #Fashion


The Lake Havasu Area Chamber of Commerce Ambassadors celebrate 28 years with Natural Tease. Dave and Nancy Leamons, owners, are happy to cover the Lake Havasu community with all their screen printing and embroidery designs. Natural Tease is a one stop shop, from their in-house design team to their custom embroidery, they do it all. You can contact Dave and Nancy at 855-4040 or stop by the shop at 1600 W Acoma Blvd #50.


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EPA Administrator's Motorcade
By Tony Scotti on April 7th, 2018
As mentioned in our Alexa flash briefing, the head of the Environmental Protection Agency, Scott Pruitt, reportedly wanted his motorcade to flash its lights and sirens to speed up trips to restaurants and airports.
Pruitt wanted his motorcade to use its lights and sirens to speed up local trips to the airport or dinner. According to the reports, Pruitt was often late during his trips in Washington and used the motorcade's warning signals to quicken his trips to his favorite restaurant.
Eric Weese, the former head of Pruitt's protective detail, the key word is former, said he unsuccessfully tried to curb the behavior, according. His reward for his candor was that he was replaced. He was replaced by Pasquale Perrotta, a former Secret Service agent who operates a private security company.
Sequoia Security
The New York Times reported that some EPA officials objected to the additional security coverage which included around the clock protection and a 20-person protective detail.
Pruitt's security detail accrued enough overtime to reach their annual maximum salary of around $160,000. During his first three months as EPA chief, Pruitt's security detail cost over $832,000, which would translate to about 3.3 Million dollars a year.
Pruitt was also provided security during family trips and sporting events. The Former EPA administrator had roughly a half-dozen people on her security staff, and was not provided protection during off-hours.
Scott Pruitt's staff asked for a bulletproof vehicle and $70,000 in bulletproof furniture for his office — the request was denied
AP sources: EPA chief spent millions on security and travel
An older article covering the same topic – Politicians Illegally Use Sirens And Flashing Lights
Photo Courtesy of Laurie Shall


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Updated timeline for conversion of NeuroVive's BTUs into shares and warrants
NeuroVive Pharmaceutical AB (publ) announces that registration of the preferential rights issue totaling SEK 94.4 m has now been completed, and provides an updated timeline for the conversion of NeuroVive's BTUs into shares and warrants.
THIS DOCUMENT IS NOT TO BE DISTRIBUTED, DIRECTLY OR INDIRECTLY, IN OR INTO THE US, AUSTRALIA, HONG KONG, JAPAN, CANADA, NEW ZEELAND, SOUTH AFRICA OR IN ANY OTHER JURISDICTION WHERE THE DISTRIBUTION OF THIS PRESS RELEASE WOULD BE SUBJECT TO LEGAL RESTRICTIONS.
The last day of trading in BTUs will be 24 May 2016, and the first day of trading in new shares and warrants (series 2016/2017:1 and series 2016/2017:2) will be 26 May 2016. The conversion of BTUs in the Euroclear system will be effected on 26 May 2016, and the new shares and warrants will appear in the relevant VP accounts on 30 May 2016.
After the completion of the new issue, NeuroVive's share capital amounts to SEK 2,472,932.25. The total number of shares after registration is 49,458,645.
Stockholm Corporate Finance AB acted as financial advisor and Advokatfirman Lindahl KB acted as legal advisor to the company in connection with the new issue. Aqurat Fondkommission AB acted as issuing institution in connection with the new issue and Laika Consulting was responsible for IR and marketing.
About NeuroVive
NeuroVive Pharmaceutical AB (publ) is a pioneer in mitochondrial medicine and a company committed to the discovery and development of highly targeted candidates that preserve mitochondrial integrity and function in areas of significant therapeutic need. NeuroVive's business approach is driven by value-adding partnerships with mitochondrial research institutions and commercial partners across the globe. NeuroVive's portfolio consists of two clinical projects in acute kidney injury (AKI) and traumatic brain injury (TBI) with candidates in clinical and preclinical development and two drug discovery platforms. The NeuroSTAT® product has orphan drug status in Europe and in the US for treatment of moderate to severe traumatic brain injury and is currently being evaluated in a study, CHIC. Ciclosporin (CicloMulsion®) is being evaluated in an on-going study, CiPRICS, in acute kidney injury during major surgery. NeuroVive's shares are listed on Nasdaq, Stockholm, Sweden.
For investor relations and media questions, please contact:
Christine Tadgell, NeuroVive, Tel: +46 (0)46 275 62 21 or ir@neurovive.com
NeuroVive Pharmaceutical AB (publ)
Medicon Village, SE-223 81 Lund, Sweden
Tel: +46 (0)46 275 62 20 (switchboard), Fax: +46 (0)46 888 83 48
info@neurovive.com, www.neurovive.com
NeuroVive Pharmaceutical AB (publ) is required to publish the information in this news release under The Swedish Securities Market Act. The information was submitted for publication on the 23 May 2016, at 17.15 CET.
Publication or distribution of this press release in certain jurisdictions may be subject to restrictions according to law and the people in jurisdictions where this press release has been made public or distributed should inform themselves and follow such legal restrictions. This press release does not contain and does not constitute or form part of an invitation to acquire or subscribe or a solicitation of any offer to buy or subscribe for shares or other securities in NeuroVive.
This press release may not be published or distributed, directly or indirectly, in or into the US, Australia, Hong Kong, Japan, Canada, New Zeeland, South Africa or in any other jurisdiction where such distribution would be prohibited by applicable law. The information in this press release may not be redistributed, reproduced or passed on in ways that conflict with applicable restrictions. Failure to comply with these restrictions may constitute a violation of the United States Securities Act of 1933 or applicable laws of other jurisdictions.
NeuroVive preferential rights issue fully subscribed
NeuroVive: Interim Report 1 Jan. 2016 to 31 Mar. 2016
Abliva develops medicines for the treatment of primary mitochondrial diseases. These congenital, rare and often very severe diseases occur when the cell's energy provider, the mitochondria, do not function properly. The portfolio includes projects at different stages and ranges from early discovery phase to clinical phase.
The Board of Directors is the company's highest administrative body subordinate to the AGM. The work of Abliva's Board of Directors is regulated by applicable laws and ordinances, and by the Board of Directors' rules of procedure, which are adopted annually.
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