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arXiv:0905.1849

A Question: Quantum Critical Phenomena in XY Spin-Chain Systems With Dzyaloshinskii-Moriya Interactions

Chuan-Jia Shan, W. W. Cheng, Ji-Bing Liu, Tang-Kun Liu, Yanxia Huang, Li, Hong

Published May 12, 2009• 1 citation

Abstract

Jordan-Wigner transformation and Bogolyubov transformation are the main steps of the diagonalization of Hamiltonian and paly an important role in the statistical mechanics calculations for one-dimensional Heisenberg spin chain model. Many methods can be exploited as a tool to detect quantum phase transition, regions of criticality and scaling behavior in the vicinity of a quantum phase transition, such as geometric phase, fidelity susceptibility, order parameter, and entanglement entropy, which have direct relation with Bogolyubov transformation. We diagonalized the Hamiltonian in XY spin-chain systems with Dzyaloshinskii-Moriya interactions, the results shows that only the energy spectrum but not the coefficients of the Bogolyubov transformation depends on DM interaction. Therefore, the DM interaction may not influence the critical magnetic field of quantum phase transitions and not induce new critical regions in the XY spin model. Moreover, we further prove the ideas by the methods of geometric phases in this model.

DOI: 10.48550/arxiv.0905.1849

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We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg XY spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the XY spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.

In this work, we address the ground-state properties of the anisotropic spin-1/2 Heisenberg XYZ chain under the interplay of magnetic fields and the Dzyaloshinskii-Moriya (DM) interaction which we interpret as an electric field. The identification of the regions of enhanced sensitivity determines criticality in this model. We calculate the Wigner-Yanase skew information (WYSI) as a coherence witness of an arbitrary two-qubit state under specific measurement bases. The WYSI is demonstrated to be a good indicator for detecting the quantum phase transitions. The finite-size scaling of coherence susceptibility is investigated. We find that the factorization line in the antiferromagnetic phase becomes the factorization volume in the gapless chiral phase induced by DM interactions, implied by the vanishing concurrence for a wide range of field. We also present the phase diagram of the model with three phases---antiferromagnetic, paramagnetic, and chiral---and point out a few common mistakes in deriving the correlation functions for the systems with broken reflection symmetry.

We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-

1/2

XY

model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.

We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic

\mathrm{XY}

spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. These pairwise quantities exhibit interesting behaviors in relation to the relative strengths of the physical parameters. For the infinite chain, we show that the quantum discord can be useful to highlight the quantum phase transition, especially for the long-distance spins, where entanglement decays rapidly. We observe nonanalyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point; interestingly, the DM interaction weakens the critical behavior in the derivatives of these correlations. While the DM interaction suppresses the standard behaviors of the

\mathrm{XY}

model, it enhances surprisingly the pairwise entanglement for the third nearest neighbor spins.

Abstract We investigate the quantum coherence of an XY spin chain with Dzyaloshinskii–Moriya interaction using a quantum renormalization group-based method, and show that the relative entropy of coherence increases with Dzyaloshinskii–Moriya interaction strength at zero temperature, as well as at finite temperature. We also study the quantum criticality of the system by making use of the relative entropy of coherence and violation of Bell inequality, and find that the first derivatives of the renormalized quantum coherence exhibit singularity near the critical point of the quantum phase transition. Finally, we explore the finite-size scaling behaviors of the derivatives of the quantum coherence at the critical point of the quantum phase transition, and obtain several universal finite-size scaling laws.