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Chinese Physics Letters

Thermal Entanglement of Anisotropic XY Chains in a Transverse Field

Xiao-Yue Zhai, Tong Pei-Qing

Published Aug 23, 2007• 5 citations
Publisher

Abstract

By using the concept of concurrence, we numerically investigate the thermal entanglement between any two nearest-neighbour spins in uniform and periodic anisotropic XY chains in a transverse field at finite temperature T . It is found that the entanglement has more than one critical temperatures on some parameter regions for uniform and periodic chains. We also discuss the behaviour of the thermal entanglement at the vicinity of quantum phase transition of periodic anisotropic XY chains and find that all the derivatives ∂ λ C have similar behaviour as that of the uniform chain.

DOI
10.1088/0256-307x/24/9/004

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By using the concept of concurrence, we numerically investigate the thermal entanglement between any two nearest-neighbour spins in uniform and periodic anisotropic XY chains in a transverse field at finite temperature T . It is found that the entanglement has more than one critical temperatures on some parameter regions for uniform and periodic chains. We also discuss the behaviour of the thermal entanglement at the vicinity of quantum phase transition of periodic anisotropic XY chains and find that all the derivatives ∂ λ C have similar behaviour as that of the uniform chain.
We study the entanglement of thermal and ground states in the Heisenberg XY spin chain with an inhomogeneous magnetic field.A general result is found that for two-qubit case,pairwise entanglement is independent of the sign of coupling constant J,magnetic field B,anisotropic parameter γ and inhomogeneous parameter b of the magnetic field.At zero absolute temperature,an analytical expression of concurrence C is given through which we show that the critical magnetic field Bc increases with the increase of inhomogeneity.At finite temperature,we show analytically for the isotropic case and numerically for the anisotropic case that the thermal entanglement can be apparently enhanced by introducing the inhomogeneity of the magnetic field.We also show that for isotropic case the critical temperature Tc is alone an increasing function of the inhomogeneous parameter b,while for anisotropic case,it is determined by both B and b.
The disentanglement evolution of bipartite spin- 1 / 2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied in this letter. The dynamical process of the entanglement is numerically and analytically investigated. We find that thermal effects can enhance disentanglement if the entangled initial state of the central spins does not in the decoherence free space. The critical phenomenon of quantum phase transitions reflected in the disentanglement can be washed out by the thermal effect eventually.
It is found that, for a periodic XY chain, the competition between periodicity and anisotropy gives rise to more than one phase-transition point at some parameter region. In this paper, the phase diagram of a period-two XY model in a transverse field is discussed. Two phase transitions, the Ising and anisotropy transitions, driven by the anisotropy parameter γ, are studied by singularities of the order parameters, the ground-state energy and the quantum entanglement. These two transitions are of second order and their traits are discussed.
The nearest-neighbor concurrence and block–block entanglement of a period-two XX chain with a transverse field h and a uniform long-range interaction I in the z -direction are studied numerically. It is found that when I > 0, the nearest-neighbor concurrence and block–block entanglement are both discontinuous at the critical points, where the system undergoes first-order quantum phase transitions. When the long-range interaction is weak , there are two critical points and . Between these two points there is a critical region, where the block–block entanglement . In one noncritical region is equal to a non-zero constant while in the other noncritical region is always zero. Furthermore, the effect of periodicity on the concurrence and block–block entanglement is discussed.
The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy Δ and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearest-neighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.