Results for the characteristics of the macroscopic thermal entanglement for integrable spin-1/2 antiferromagnetic chain models with multispin interactions in the thermodynamic limit are presented. Such interactions cause quantum-phase transitions to incommensurate phases with partial spontaneous magnetization. We have derived exact equations, which determine the thermal and magnetic field behavior of the concurrence of spin chains. The analysis of these equations shows that there exists a critical temperature, below which the thermal entanglement of considered spin chains is nonzero. We have shown that at those quantum-phase transitions, caused by multispin interactions, the thermal entanglement is reduced. Also, we have shown that the thermal entanglement is reduced due to nonzero magnetization of spin chains in the ground state, caused by multispin interactions.
The entanglement properties of a three-spin XXZ Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at Δ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J / T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.
We investigate the entanglement properties of a one-dimensional chain of qubits coupled via nearest-neighbor spin-spin interactions. The entanglement measure used is the -concurrence, which is distinct from other measures on spin chains such as bipartite entanglement in that it can quantify ``global'' entanglement across the spin chain. Specifically, it computes the overlap of a quantum state with its time-reversed state. As such, this measure is well suited to study ground states of spin-chain Hamiltonians that are intrinsically time-reversal-symmetric. We study the robustness of -concurrence of ground states when the interaction is subject to a time-reversal antisymmetric magnetic field perturbation. The -concurrence in the ground state of the isotropic model is computed and it is shown that there is a critical magnetic field strength at which the entanglement experiences a jump discontinuity from the maximum value to zero. The -concurrence for thermal mixed states is derived and a threshold temperature is computed below which the system has nonzero entanglement.
We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We prove here that among the considered thermodynamic and thermal parameters, solely heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should be investigated by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.
Abstract In this paper we investigate the ability of the generalized concurrence as a quantum entanglement measure to describe the quantum and thermal phase transitions in the spin-1 Heisenberg model with bilinear and biquadratic interactions and single-ion anisotropy terms, under a magnetic field. Calculations are performed for two and three spin chains based on the exact diagonalization method. We show that in the near vicinity of the zero temperature, the generalized concurrence changes abruptly from a finite non-zero value to zero by changing the parameters of the model. This is signature of a quantum phase transition that is carefully justified by studying the thermodynamic functions such as magnetization, particle number, particle susceptibility and magnetic susceptibility. The critical points are found and various ordered phases are discussed.
The thermal pairwise entanglement (TE) of the
S=1/2 XY chain in a transverse magnetic field is exactly resolved by means of the Jordan-Wigner transformation in the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. It is found that the TE vanishes at a fixed point with temperature ${T}_{c}\ensuremath{\simeq}0.484\text{ }3J$, which is independent of the magnetic field. A thermal quantity is proposed to witness the entangled state. Furthermore, the TE of the
S=1/2 antiferromagnetic-ferromagnetic (AF-F) Heisenberg chain is studied by the transfer-matrix renormalization-group method. The TEs of the spins coupled by AF and F interactions are found to behave distinctively. The vanishing temperature of the field-induced TE of the spins coupled by F interactions is observed dependent on the magnetic field. The results are further confirmed and analyzed within a mean-field framework.
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
21, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength
J1,
J2, 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=21 antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with
J2=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
Tc below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron
(J1=J2,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
TE 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.