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Acta Physica Sinica

Thermal entanglement of mixed spin XY systems

Wang Lu-Shun, Jiang Hui, Xiang-Mu Kong

Published Jan 1, 2012• 2 citations
Publisher

Abstract

In this article, we investigate thermal entanglements of the two-site, three-site and four-site mixed spin (1/2,1) XYsystems. The entanglement versus temperature and external magnetic field is discussed. It is found that the entanglements decrease monotonically as temperature increases in the presence and absence of a weak external magnetic field. For the two-site and four-site XY systems, thermal entanglements disappear at the same temperature which is called critical temperature no matter in the ferromagnetic case or antiferromagnetic. It also shows that the critical temperature is independent of external magnetic field. For the three-site system, the corresponding critical temperature is also irrelevant to external magnetic field, while the critical temperature for the ferromagnetic case is higher than that for the antiferromagnetic case. The entanglement of XY systems can develop a few stable platform in an environment of low temperature, but the entanglement vanishes when external magnetic field exceeds some critical value. In this article, we also analyze the difference in thermal entanglement between mixed-spin system and single-spin system, and find that there exists multi-level level crossing in the mixed-spin system.

DOI
10.7498/aps.61.240304

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In this article, we investigate thermal entanglements of the two-site, three-site and four-site mixed spin (1/2,1) XYsystems. The entanglement versus temperature and external magnetic field is discussed. It is found that the entanglements decrease monotonically as temperature increases in the presence and absence of a weak external magnetic field. For the two-site and four-site XY systems, thermal entanglements disappear at the same temperature which is called critical temperature no matter in the ferromagnetic case or antiferromagnetic. It also shows that the critical temperature is independent of external magnetic field. For the three-site system, the corresponding critical temperature is also irrelevant to external magnetic field, while the critical temperature for the ferromagnetic case is higher than that for the antiferromagnetic case. The entanglement of XY systems can develop a few stable platform in an environment of low temperature, but the entanglement vanishes when external magnetic field exceeds some critical value. In this article, we also analyze the difference in thermal entanglement between mixed-spin system and single-spin system, and find that there exists multi-level level crossing in the mixed-spin system.
We numerically investigate thermal entanglement of the spins (1/2,1) and (1/2,1/2) in the three-mixed (1/2,1,1/2) anisotropic Heisenberg XXZ spin system on a simple triangular cell under an inhomogeneous magnetic field. We show that the external magnetic field induces strong plateau formation in pairwise thermal entanglement for fixed parameters of Hamiltonian in the case of the ferromagnetic and anti-ferromagnetic interactions. We also observe an unexpected critical point at finite temperature in the thermal entanglement of the spins (1/2,1) for antiferromagnetic case while the entanglement of the spins (1/2,1) for ferromagnetic case and the entanglement of the spins (1/2,1/2) for both ferromagnetic and antiferromagnetic cases almost decays exponentially to zero with increasing temperature. The critical point in entanglement of the spins (1/2,1) for antiferromagnetic case may be signature of the quantum phase transition at finite temperature.
We numerically investigate thermal entanglement of the spins (1/2,1) and (1/2,1/2) in the three-mixed (1/2,1,1/2) anisotropic Heisenberg XXZ spin system on a simple triangular cell under an inhomogeneous magnetic field. We show that the external magnetic field induces strong plateau formation in pairwise thermal entanglement for fixed parameters of Hamiltonian in the case of the ferromagnetic and anti-ferromagnetic interactions. We also observe an unexpected critical point at finite temperature in the therm al entanglement of the spins (1/2,1) for antiferromagnetic case while the entanglement of the spins (1/2,1) for ferromagnetic case and the entanglement of the spins (1/2,1/2) for both ferromagnetic and antiferromagnetic cases almost decays exponentially to zero with increasing temperature. We conclude that this critical point in entanglement of the spi ns (1/2,1) for antiferromagnetic case indicates the presence of the quantum phase transition at finite temperature.
We numerically investigate the thermal entanglements of spins (1/2, 1) and spins (1/2, 1/2) in the three-mixed (1/2, 1, 1/2) anisotropic Heisenberg XXZ spin system on a simple triangular cell under an inhomogeneous magnetic field. We show that the external magnetic field induces strong plateau formation in the pairwise thermal entanglement for fixed parameters of the Hamiltonian in the cases of ferromagnetic and antiferromagnetic interactions. We also observe an unexpected critical point at finite temperature in the thermal entanglement of spins (1/2, 1) for the antiferromagnetic case, while the entanglement of spins (1/2, 1) in the ferromagnetic case and the entanglement of spins (1/2, 1/2) in both ferromagnetic and antiferromagnetic cases almost decay exponentially to zero with increasing temperature. The critical point in the entanglement of spins (1/2, 1) in the antiferromagnetic case may be a signature of the quantum phase transition at finite temperature.
We study and compare the persistence of bipartite entanglement (BE) and multipartite entanglement (ME) in one-dimensional and two-dimensional spin XY models in an external transverse magnetic field under the effect of thermal excitations. We compare the threshold temperature at which the entanglement vanishes in both types of entanglement. We use the entanglement of formation as a measure of the BE and the geometric measure to evaluate the ME of the system. We have found that in both dimensions in the anisotropic and partially anisotropic spin systems at zero temperatures, all types of entanglement decay as the magnetic field increases but are sustained with very small magnitudes at high field values. Also we found that for the same systems, the threshold temperatures of the nearest neighbour (nn) BEs are higher than both of the next-to-nearest neighbour BEs and MEs and the three of them increase monotonically with the magnetic field strength. Thus, as the temperature increases, the ME and the far parts BE of the system become more fragile to thermal excitations compared to the nn BE. For the isotropic system, all types of entanglement and threshold temperatures vanish at the same exact small value of the magnetic field. We emphasise the major role played by both the properties of the ground state of the system and the energy gap in controlling the characteristics of the entanglement and threshold temperatures. In addition, we have shown how an inserted magnetic impurity can be used to preserve all types of entanglement and enhance their threshold temperatures. Furthermore, we found that the quantum effects in the spin systems can be maintained at high temperatures, as the different types of entanglements in the spin lattices are sustained at high temperatures by applying sufficiently high magnetic fields.
Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.