Influence of magnetic field on swap operation in Heisenberg XXZ model

We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubits system. We have considered the anisotropic Heisenberg (XXZ) model in the presence of Dzyaloshinskii–Moriya (DM) interaction in addition to the Ising model in a magnetic field with DM interaction. We have found that the increment of DM interaction and magnetic field can enhance and reduce the entanglement of the system. We have shown that the non-symmetric pairwise state has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise one. For the negative anisotropy, the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy, it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in detail. The most remarkable result appears at zero temperature where the three-qubits ground state entanglement of the system (in spite of two-qubits counterpart) shows the fingerprint of the quantum phase transition for a system of infinite number of qubits.

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THERMAL AND NON-UNIFORM MAGNETIC QUANTUM DISCORD IN THE TWO-QUBIT HEISENBERG XXZ MODEL

Modern Physics Letters B ◽

10.1142/s021798491150028x ◽

2012 ◽

Vol 26 (05) ◽

pp. 1150028 ◽

Cited By ~ 2

Author(s):

RUI-HUA XIAO ◽

ZHAN-YING GUO ◽

JIAN-XING FANG

Keyword(s):

Magnetic Field ◽

Critical Temperature ◽

Uniform Magnetic Field ◽

Quantum Discord ◽

Critical Magnetic Field ◽

Thermal Entanglement ◽

Xxz Model ◽

Analytical Expressions ◽

Heisenberg Xxz Model

The thermal quantum discord (QD) is investigated in the two-qubit anisotropic Heisenberg XXZ model under an external non-uniform magnetic field along the Z-axis. We obtain the analytical expressions of the thermal QD and thermal entanglement measured by concurrence (C). It shows that for any temperature T, QD gradually decreases with the increase of non-uniform magnetic field |b|, in some regions where C increases while QD decreases. It is also found that thermal quantum discord does not vanish at finite temperatures, but concurrence vanishes completely at a critical temperature. It is shown that for a higher value of JZ, the system has a stronger QD. There is a critical magnetic field B c , which increases with the increasing b. QD decay monotonically (for B < B c ) when temperature T increases, or initially increases to some peaks and then decrease (for B > B c ).

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LATTICE ALGEBRAS AND THE HIDDEN SYMMETRY OF THE 2D ISING MODEL IN A MAGNETIC FIELD

International Journal of Modern Physics A ◽

10.1142/s0217751x91002422 ◽

1991 ◽

Vol 06 (28) ◽

pp. 5127-5153 ◽

Cited By ~ 7

Author(s):

DAN LEVY

Keyword(s):

Magnetic Field ◽

Ising Model ◽

External Magnetic Field ◽

Lattice Models ◽

Natural Generalization ◽

Xxz Model ◽

Affine Hecke Algebra ◽

Finite Dimensional ◽

Hidden Symmetry ◽

Boundary Terms

Lattice algebras are defined and used to study the symmetries of 2D lattice models. New and interesting examples of such algebras are provided by the affine Hecke algebra, owing to the possibility of constructing braid generators out of its generators. I propose an Ansatz for the braid generators and derive some solutions. A particular finite-dimensional quotient is shown to be a natural generalization of the Temperley-Lieb-Jones algebra. It is used to give a unified picture of known and unknown symmetries of the spin-½ xxz model with boundary terms. The Ising model in an external magnetic field is also a representation of this quotient.

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Thermal Quantum Discord in Anisotropic Heisenberg XXZ Model with Dzyaloshinskii–Moriya Interaction

Communications in Theoretical Physics ◽

10.1088/0253-6102/54/1/12 ◽

2010 ◽

Vol 54 (1) ◽

pp. 60-66 ◽

Cited By ~ 22

Author(s):

Chen Yi-Xin ◽

Yin Zhi

Keyword(s):

Quantum Discord ◽

Xxz Model ◽

Moriya Interaction ◽

Heisenberg Xxz Model

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