具有Dzyaloshinskii-Moriya相互作用的调制XY自旋链的Lee-Yang零点：零轮廓拓扑与量子相图重构

中文摘要 AI 辅助

我们研究了在复横场平面中具有Dzyaloshinskii-Moriya (DM)相互作用的非均匀各向异性XY自旋链的Lee-Yang零点 (LYZ)，重点关注它们与量子相变的基本联系。我们系统地研究了长度为5和8的均匀链、周期2和周期3调制链以及Fibonacci准周期链。随着DM耦合强度$D$的增加，LYZ在复平面上表现出定性不同的拓扑演化：均匀链的复零点向实轴坍缩；周期链要么在所有零点变为实数之前出现闭合零轮廓的分叉，要么出现复零点的单次重现；准周期链则表现出复零点的反复湮灭和复兴。解析推导表明，这种多样化的行为源于DM诱导的折叠能带位移以及粒子-空穴能带交叉处各向异性配对对零点位置的调制。我们的结果建立了LYZ拓扑与能带形变之间的直接对应关系：零点与实轴的孤立接触点对应于离散的量子临界场，而连续实零点区间直接识别无能隙手性相。因此，除了定位相边界之外，LYZ还能区分特征相，并作为能带折叠和相图重构的直观探针。

英文摘要

We investigate the Lee--Yang zeros (LYZ) of inhomogeneous anisotropic XY spin chains with Dzyaloshinskii--Moriya (DM) interactions in the complex transverse-field plane, focusing on their fundamental connection to quantum phase transitions. We systematically study uniform chains, period-2 and period-3 modulated chains, and Fibonacci quasiperiodic chains of lengths 5 and 8. As the DM coupling strength $D$ increases, the LYZ exhibit qualitatively distinct topological evolutions on the complex plane: the complex zeros of the uniform chain collapse toward the real axis; periodic chains feature either bifurcation of closed zero contours before all zeros become real or a single re-emergence of complex zeros; quasiperiodic chains exhibit repeated annihilation and revival of complex zeros. Analytical derivations demonstrate that this diverse behavior originates from DM-induced shifts of folded bands and the modulation of zero positions by anisotropic pairing at particle--hole band crossings. Our results establish a direct correspondence between LYZ topology and band deformation: isolated contact points of zeros with the real axis correspond to discrete quantum critical fields, while continuous real-zero intervals directly identify gapless chiral phases. Accordingly, beyond locating phase boundaries, LYZ can distinguish characteristic phases and serve as an intuitive probe for band folding and phase diagram restructuring.

发表机构

• Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术学院物质科学与光电工程中心）
• School of Physics, Hangzhou Normal University（杭州师范大学物理学院）

机构由 AI 辅助整理，请以论文原文为准。