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arXiv:1403.3437 · Physical Review A

Induced effects of the Dzyaloshinskii-Moriya interaction on the thermal entanglement in spin-1/2 Heisenberg chains

E. Mehran, S. Mahdavifar, Rouhollah Jafari

Published Apr 8, 2014• 39 citations
arXivHTMLPDF

Abstract

The nearest-neighbor spins in the one-dimensional spin-1/2 $XX$ model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field, ${h}_{c}$. Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.

DOI
10.1103/physreva.89.042306

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We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including D z and D x , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters ( D z and D x ) have remarkably different influences on the entanglement. Different from the case D z , there is the non-monotonic variation of the concurrence with temperature in the case D x , and additionally the DM interaction D x can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case D x is larger than that of the case D z .
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In this paper, we study the property of thermal entanglement in four-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered, and investigate the pairwise concurrences of two nearest-neighbor qubits and two next-neighbor qubits to study this entanglement property. The result shows that for the two-next-neighbor-qubit case, there exists pairwise concurrence neigher in ferromagnetic model nor in antiferromagnetic model; but for the two-nearest-neighbor-qubits case, the DM interaction and the parameter of the anisotropy exchange coupling have a significant influence on the pairwise entanglement and critical temperature Tc. Moreover, the pairwise concurrence will decrease with the increase of temperature. When the temperature execeds its critical value, the pairwise concurrence disappears. Therefore, the pairwise entanglement can be controlled and enhanced by choosing the appropriate parameters of the DM interaction and the anisotropy exchange coupling.
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