具有交错Dzyaloshinskii--Moriya相互作用的非厄米XY链的量子相变与量子信息表征

中文摘要 AI 辅助

我们利用量子信息方法研究了一维具有交错Dzyaloshinskii--Moriya (DM)相互作用的非厄米XY链的相图。通过交替局域自旋旋转变换，该模型被映射到一条标准的无DM的XY链上，变换后的哈密顿量展现出旋转-时间反演（$\RT$）对称性。将关联函数分析与标准XY链的已知相结果相结合，我们构建了当前系统的相图。我们进一步采用基于量子信息的量，系统地评估它们在表征该非厄米系统中量子相变方面的性能。我们的结果表明，单位点纠缠只能探测到Luttinger液体（LL）—顺磁（PM）相变，该相变对应于$\RT$对称性恢复的例外边界。相比之下，量子失谐（QD）和量子相干性（QC）能够识别出两个相边界：除了定位例外边界外，它们的二阶导数还能分辨出$\RT$破缺区域内的铁磁（FM）—LL相变。此外，沿不同方向测量QC能够捕捉到DM诱导的两个子晶格之间的相对旋转，从而将交错DM链与具有相同有效参数的零DM链区分开来。

英文摘要

We investigate the phase diagram of a non-Hermitian XY chain with staggered Dzyaloshinskii--Moriya (DM) interactions using quantum-information methods. Through an alternating local-spin-rotation transformation, the model is mapped onto a standard DM-free XY chain, and the resulting transformed Hamiltonian exhibits rotation--time-reversal ($\RT$) symmetry. Combining correlation-function analysis with known phase results of the standard XY chain, we construct the phase diagram for the present system. We further adopt quantum-information-based quantities to systematically assess their performance in characterizing quantum phase transitions within this non-Hermitian system. Our results show that single-site entanglement can only detect the Luttinger-liquid (LL)--paramagnetic (PM) phase transition, which corresponds to the exceptional boundary across which $\RT$ symmetry is restored. In contrast, quantum discord (QD) and quantum coherence (QC) identify both phase boundaries: in addition to locating the exceptional boundary, their second-order derivatives resolve the ferromagnetic (FM)--LL transition inside the $\RT$-broken region. Moreover, measurements of QC along different directions capture the DM-induced relative rotation between the two sublattices, thereby distinguishing the staggered-DM chain from a zero-DM chain with identical effective parameters.

发表机构

• University of Chinese Academy of Sciences（中国科学院大学）
• Hangzhou Normal University（杭州师范大学）

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