Entropic uncertainty relations and quantum coherence in the two-dimensional XXZ spin model with Dzyaloshinskii–Moriya interaction

Yu-Yan Fang, Chengjie Zhang and Jin-Ming Liu

Physica A: Statistical Mechanics and its Applications, 2024, vol. 650, issue C

Abstract: Quantum renormalization group (QRG) is a tractable method for studying the criticalities of one-dimensional (1D) and two-dimensional (2D) many-body systems. By employing the QRG method, we first derive the effective Hamiltonian and QRG equations of a 2D XXZ model with Dzyaloshinskii–Moriya (DM) interaction analytically. The linear-entropy-based uncertainty, the quantum discord (QD), and the multipartite quantum coherence based on the square root of the quantum Jensen–Shannon divergence of the 2D XXZ model are then studied as the indicators of quantum phase transitions (QPTs). The nonanalytic and scaling behaviors of the uncertainty, QD and quantum coherence are also analyzed through numerical calculations. Moreover, we investigate the effect of the easy-axis anisotropy parameter and DM interaction on the QPT. We find that the uncertainty, QD, and quantum coherence can all be utilized to detect QPTs. Our findings could shed new light on the observable of the QPT of the many-body system with the uncertainty and quantum coherence, and enrich the application of QRG method to Heisenberg spin models.

Keywords: Quantum renormalization group; Entropic uncertainty relations; Quantum coherence; Quantum phase transition (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:650:y:2024:i:c:s0378437124004989

DOI: 10.1016/j.physa.2024.129989

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