Abstract We briefly review recent work on entanglement with particular emphasis on its behaviour in interacting spin systems. As already pointed out by several authors a general understanding of the properties of entanglement in condensed matter systems may lead to a deeper comprehension of both dynamics and thermodynamics of many‐body systems. After a brief resume of known means to identify and quantify entanglement, we take interacting spins on a network as an example. We briefly discuss critical properties of entanglement, if the system undergoes a quantum phase transition, and some aspects of its dynamical behaviour.Abstract We briefly review recent work on entanglement with particular emphasis on its behaviour in interacting spin systems. As already pointed out by several authors a general understanding of the properties of entanglement in condensed matter systems may lead to a deeper comprehension of both dynamics and thermodynamics of many‐body systems. After a brief resume of known means to identify and quantify entanglement, we take interacting spins on a network as an example. We briefly discuss critical properties of entanglement, if the system undergoes a quantum phase transition, and some aspects of its dynamical behaviour.

Annalen der PhysikFeb 2, 20050 citations

Entanglement properties in mixed spin- systems

Huaixiang Huang, Xiaoguang Wang, Zhe Sun +1 more

Physica A Statistical Mechanics and its ApplicationsJan 28, 200811 citations

Entanglement properties of XX model with three spin interactions

Xiu Zhang

Using the Concurrence criterion,we investigate the entanglement properties of XX model with three spin interactions.The effects of the three spin interaction J_2 and temperature T on the entanglement are discussed in both ferromagnetic and anti-ferromagnetic cases.Our results show that J_2 enhances the entanglement of the system,but the extent is difference for ferromagnetic and anti-ferromagnetic cases.J_2 also affects the critical temperature T_C,at which the entanglement disappears.T_C decreases with the increasing of J_2.Moreover,our results also indicate that the maximal entanglement increases with the decreasing of system temperature T.In addition,we also investigate the pairwise entanglement of the eigenstates of the Hamiltonian and discuss the ground-state entanglement.We obtain the quantum critical point at which the quantum phase transition takes place.Using the Concurrence criterion,we investigate the entanglement properties of XX model with three spin interactions.The effects of the three spin interaction J_2 and temperature T on the entanglement are discussed in both ferromagnetic and anti-ferromagnetic cases.Our results show that J_2 enhances the entanglement of the system,but the extent is difference for ferromagnetic and anti-ferromagnetic cases.J_2 also affects the critical temperature T_C,at which the entanglement disappears.T_C decreases with the increasing of J_2.Moreover,our results also indicate that the maximal entanglement increases with the decreasing of system temperature T.In addition,we also investigate the pairwise entanglement of the eigenstates of the Hamiltonian and discuss the ground-state entanglement.We obtain the quantum critical point at which the quantum phase transition takes place.

Journal of Atomic and Molecular PhysicsJan 1, 20100 citations

New entanglement properties in systems of higher-spin particles

Jay Lawrence, Mario Gaeta, Andrei Klimov

Bulletin of the American Physical SocietyFeb 27, 20120 citations

Thermal entanglement properties of small spin clusters

Indrani Bose, Amit Tribedi

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude $\frac{1}{2}$ , in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength ${J}_{1}$ , ${J}_{2}$ , and $K$ , respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a $S=\frac{1}{2}$ antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with ${J}_{2}=0$ , $K=0$ , in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature ${T}_{c}$ below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron $({J}_{1}={J}_{2},K=0)$ ---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature ${T}_{E}$ below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude $\frac{1}{2}$, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength ${J}_{1}$, ${J}_{2}$, and $K$, respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a $S=\frac{1}{2}$ antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with ${J}_{2}=0$, $K=0$, in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature ${T}_{c}$ below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron $({J}_{1}={J}_{2},K=0)$---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature ${T}_{E}$ below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.

arXiv:cond-mat/0503170Physical Review AAug 15, 200557 citations

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude

\frac{1}{2}

, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength

{J}_{1}

{J}_{2}

, and

K

, respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a

S=\frac{1}{2}

antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with

{J}_{2}=0

K=0

, in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature

{T}_{c}

below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron

({J}_{1}={J}_{2},K=0)

---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature

{T}_{E}

below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.