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Physical Review A

Entanglement patterns and pure quantum correlations in the Heisenberg XY model

F. B. M. dos Santos, R. M. Dias, A. M. S. Macêdo

Published Mar 24, 2009• 5 citations
Publisher

Abstract

We investigate the possibility of the existence of different types of thermal entanglement in the two-spin Heisenberg $XY$ model, which are distinguished by the behavior of the concurrence as a function of the model parameters. Singularities in the temperature threshold for thermal entanglement and in the ground-state energy as a function of the model parameters are used to construct diagrams containing boundary lines separating the several types of thermal entanglement in the system, showing an unexpected rich structure. We discuss a procedure to extract a pure quantum component from the spin-correlation function at arbitrary temperatures, by using the explicit form of the decomposition that minimizes the concurrence, and show that it is highly sensitive to the different patterns of thermal entanglement.

DOI
10.1103/physreva.79.032329

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We investigate the possibility of the existence of different types of thermal entanglement in the two-spin Heisenberg XYXYXY model, which are distinguished by the behavior of the concurrence as a function of the model parameters. Singularities in the temperature threshold for thermal entanglement and in the ground-state energy as a function of the model parameters are used to construct diagrams containing boundary lines separating the several types of thermal entanglement in the system, showing an unexpected rich structure. We discuss a procedure to extract a pure quantum component from the spin-correlation function at arbitrary temperatures, by using the explicit form of the decomposition that minimizes the concurrence, and show that it is highly sensitive to the different patterns of thermal entanglement.
We elucidate the finite temperature entanglement properties of N=9N=9N=9 qubits Heisenberg XXXXXX and XXZXXZXXZ models under the presence of a polarized magnetic field in xzxzxz plane by means of concurrence concept. We perform a systematic analysis for a wide range of the system parameters. Our results suggest that the global phase regions which separate the entangled and non-entangled regions sensitively depend upon the spin-spin interaction term of the z−z-z− component of two neighboring spins Jz/JxJ_{z}/J_{x}Jz​/Jx​, temperature as well as polarized magnetic field components. Thereby, we think that polarized magnetic field can be used a control parameter to determine the amount of thermal entanglement between pair of qubits for different temperatures and spin-spin interaction terms. Moreover, it has been found that the nearest-neighbor pair of qubits does not point out a re-entrant type entanglement character when one only deals with the nearest-neighbor pair of qubits. However, as one considers next-nearest neighbor pair of qubits, it is possible to see the evidences of re-entrant type entanglement behaviors.
We study the robustness of multipartite entanglement of the ground state of the one-dimensional spin-12\frac{1}{2}21​ XYXYXY model with a transverse magnetic field in the presence of thermal excitations by investigating a threshold temperature, below which the thermal state is guaranteed to be entangled. We obtain the threshold temperature based on the geometric measure of entanglement of the ground state. The threshold temperature reflects three characteristic lines in the phase diagram of the correlation function. Our approach reveals a region where multipartite entanglement at zero temperature is high but is thermally fragile and another region where multipartite entanglement at zero temperature is low but is thermally robust.
Quantum entanglement is one of the most fascinating types of correlation that can be shared only among quantum systems. The Heisenberg chain is one of the simplest quantum chains which exhibits a reach entanglement feature, due to the Heisenberg interaction is quantum coupling in the spin system. The two particles were coupled trough XYZ coupling or simply called as two-qubit XYZ spin, which are the responsible for the emergence of thermal entanglement. These two-qubit operators are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. We will discuss two-qubit thermal entanglement effect on Ising-XYZ diamond chain structure. The concurrence could be obtained straightforwardly in terms of two-qubit density operator elements, using this result, we study the thermal entanglement, as well as the threshold temperature where entangled state vanishes. The present model displays a quite unusual concurrence behavior, such as, the boundary of two entangled regions becomes a disentangled region, this is intrinsically related to the XY-anisotropy in the Heisenberg coupling. Despite a similar property had been found for only two-qubit, here we show in the case of a diamond chain structure, which reasonably represents real materials.
Thermal entanglement of spins are investigated in the several Heisenberg models by using of various entanglement measures, and we will evaluate the quantity of thermal entanglement with different parameters of the system (such as, magnetic field, temperture, impurity and different components of interaction). In part of proceduring, we will show that entanglement between two spins have a gaussian profile at the low temperature, and we show that there exists a relation between the QPT and the entanglement in three – qubit Heisenberg chain under the effect of impurity. In fact, QPT is the structure change in property of the ground state at the many–body system, which occures at absolute zero temperature and is purely driven by quantum fluctuation. This transitions appear with the change of a physical parameter. Thus we expect that phase transitions and critical behavior of systems can be explained by entanglement. Also, we investigate the entanglement in pure and thermal cluster states and pay attention to entanglement generation from thermal spin states inputed in a beam spliter. Then, thermal entanglement of Bosonic atoms are investigated in an optical lattices with nonlinear couplings and inhomogeneous magnetic field parameters by using of Negativity measure. We understand from the receiving results that nonlinear coupling coefficient support to entanglement can be improve under antiparalel magnetic field. Finally, we investigate quantum Teleportation at the Heisenberg model in presence of system impurity, as the result of quantum entanglement. We will demonstrate that the Fidelity average, as the measure for evaluation quantum Teleportation, can be controled by modulating magnetic field and impurity parameter Keywords: Beam Spliter, Closest Separable State, Concurrence, Entanglement, Fidelity Average, Generation Entanglement, Ground State Entanglement, Heisenberg Model, Impurity, Inhomogenous, Negativity, Nonlinear Coupling, Normal Lattice, Pure Cluster States, Pure state, Quantum Phase Transition, Quantum Teleportation, Thermal Entanglement.
We investigate the thermal entanglement in the two-qubit Heisenberg XY model with a nonuniform magnetic field. Concurrence, the measurement of entanglement, is calculated. The behavior of concurrence is present at three different cases. Contrary to the uniform magnetic field case, we find that the entanglement and the critical temperature TC{T}_{C}TC​ may be enhanced under a nonuniform magnetic field.
The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling JJJ are studied as functions of temperature and JJJ. The two concurrences exhibit a different dependence on JJJ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.