交错虚Dzyaloshinskii--Moriya相互作用诱导的XY模型中的非厄米量子相变
Non-Hermitian quantum phase transitions in the XY model induced by staggered imaginary Dzyaloshinskii--Moriya interaction
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- 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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中文总结 AI 辅助
该研究通过交错虚DM相互作用驱动非厄米XY链，提出基于RT对称性的相干度量，识别RT对称破缺转变并解析所有磁相边界。
中文摘要 AI 辅助
我们研究了横向场$XY$链中由交错虚Dzyaloshinskii--Moriya（DM）相互作用驱动的非厄米量子相变。借助交错非幺正变换，我们精确对角化了哈密顿量。对于$D<1$，该过程将非厄米模型映射到标准厄米$XY$链，从而可以解析推导出完整的相边界。参数线$D=1$形成具有合并准粒子本征值和本征矢量的例外边界，而整个$D>1$区域则落入包含两个不同$z$-铁磁相的$\mathcal{RT}$对称性破缺相。我们检验了常见的量子信息探针，并表明传统度量（如纠缠熵、量子失协和量子相干性）无法捕捉$\mathcal{RT}$对称性破缺转变。为解决这一缺陷，我们提出了一种基于$\mathcal{RT}$对称性和复共轭本征对相关性的新型相干度量$\widetilde{\mathrm{QC}}_{\max}^{\rm LR}$。$\widetilde{\mathrm{QC}}_{\max}^{\rm LR}$嵌入了左右本征态的内在非厄米信息，能够可靠地识别$\mathcal{RT}$对称性破缺转变，并准确分辨所有磁相边界。
英文摘要
We investigate non-Hermitian quantum phase transitions driven by staggered imaginary Dzyaloshinskii--Moriya (DM) interactions in a transverse-field $XY$ chain. By virtue of a staggered nonunitary transformation, we exactly diagonalize the Hamiltonian. For $D<1$, this procedure maps the non-Hermitian model onto a standard Hermitian $XY$ chain, allowing analytical derivation of the full phase boundaries. The parameter line $D=1$ forms an exceptional boundary with coalesced quasiparticle eigenvalues and eigenvectors, while the entire $D>1$ regime falls into the $\mathcal{RT}$-symmetry-broken phase containing two distinct $z$-ferromagnetic phases. We examine common quantum-information probes and show that conventional measures, such as entanglement entropy, quantum discord, and quantum coherence, fail to capture the $\mathcal{RT}$ symmetry-breaking transition. To address this deficiency, we propose a novel coherence measure $\widetilde{\mathrm{QC}}_{\max}^{\rm LR}$ based on $\mathcal{RT}$ symmetry and complex-conjugate eigenpair correlations. Embedding intrinsic non-Hermitian information of left and right eigenstates, $\widetilde{\mathrm{QC}}_{\max}^{\rm LR}$ reliably identifies the $\mathcal{RT}$ symmetry-breaking transition and accurately resolves all magnetic phase boundaries.
