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[论文解读] Spontaneous Parity Breaking in Quantum Antiferromagnets on the Triangular Lattice

Songtai Lv, Yuchen Meng|arXiv (Cornell University)|Feb 5, 2026
Quantum many-body systems被引用 0
一句话总结

这篇论文提出一种基于奇偶性的用于应力诱导相在三角格点 TLXXZ 模型的经验法则，显示在某些区域自发奇偶破缺，在磁场下奇偶性恢复，并将改进的 CTMRG 方法扩展应用于双层系统的结果。

ABSTRACT

Frustration on the triangular lattice has long been a source of intriguing and often debated phases in many-body systems. Although symmetry analysis has been employed, the role of the seemingly trivial parity symmetry has received little attention. In this work, we show that phases induced by frustration are systematically shaped by an implicit rule of thumb associated with spontaneous parity breaking. This principle enables us to anticipate and rationalize the regimes and conditions under which nontrivial phases emerge. For the spin-$S$ antiferromagnetic XXZ model, we demonstrate that a controversial parity-broken phase appears only at intermediate values of $S$. In bilayer systems, enhanced frustration leads to additional phases, such as supersolids, whose properties can be classified by their characteristic parity features. Benefiting from our improved tensor network contraction techniques, we confirm these results through large-scale tensor-network calculations. This study offers an alternative viewpoint and a systematic approach for examining the interplay between spin, symmetry, and frustration in many-body systems.

研究动机与目标

  • 为在三角格点上围绕应力诱导相的自发性奇偶破缺提供以奇偶性为中心的组织原理。
  • 确定 TLXXZ 模型中自旋相关的奇偶破缺发生的自旋区间。
  • 将分析扩展到双层系统以识别超固态相中的奇偶结构。
  • 开发并应用加速的 CTMRG 收缩方案以实现大尺度张量网络模拟。
  • 阐明 Fan 相的存在性及其参数区间及其与奇偶性的关系。

提出的方法

  • 提出带三晶胞单元的投影张量单纯形态态（PESS）猜想。
  • 对 TLXXZ 模型使用改进的角落传输矩阵重正化群（CTMRG）收缩方案。
  • 计算 S = 1/2、1、和 5/2 在 eta-h 平面的基态相图。
  • 通过将亚晶格 A、B、C 置于奇偶操作下来分析奇偶性质。
  • 扩展到双层 TLXXZ 以研究二聚化、磁化台阶和超固态相。
  • 通过其奇偶特征和自旋配置来识别和分类各相。
Figure 1: CTMRG procedure for the triangular lattice. (a–c) Three blocks arising from the triangular-lattice periodicity, each composed of local tensors $M_{i}$ ( $i$ = $A$ , $B$ , $C$ ) together with their associated edge tensors $L_{i}^{\mu}$ ( $\mu=$ $l$ , $d$ , $r$ , $u$ ) and corner tensors $L_
Figure 1: CTMRG procedure for the triangular lattice. (a–c) Three blocks arising from the triangular-lattice periodicity, each composed of local tensors $M_{i}$ ( $i$ = $A$ , $B$ , $C$ ) together with their associated edge tensors $L_{i}^{\mu}$ ( $\mu=$ $l$ , $d$ , $r$ , $u$ ) and corner tensors $L_

实验结果

研究问题

  • RQ1在不同自旋 S 的情况下，三角格点 AF TLXXZ 模型中的挫折是否会导致自发奇偶破缺？
  • RQ2外场沿纵向场 h_z 如何影响奇偶对称性和相的稳定性？
  • RQ3Fan 相在不同 S 情况下与奇偶性的关系及其存在性和区间？
  • RQ4双层耦合如何改变相结构和奇偶性性质，包括超固态？
  • RQ5一条加速 CTMRG 方法是否能可靠地捕捉这些体系的大尺度张量网络结果？

主要发现

  • 在挫折诱导的自旋有序相中，存在一个基于经验的奇偶原则：奇偶性自发破缺，增加纵向磁场趋向于恢复奇偶性。
  • 对于 S = 1/2，Fan 相不存在；奇偶破缺相包括零场的 120° 状态、伞形、UUD 和 Y，相位的 FM 和 V 保持奇偶性。
  • 随着 S 增大，Fan 相可出现在伞形与 V 之间，与在更大自旋系统中从 Fan 到 V 的奇偶性恢复转变一致。
  • 在双层体系中，增强的挫折导致额外相如超固态相的出现，具有包括奇偶 a 与奇偶 b 区分在内的复杂奇偶结构。
  • 改进的 CTMRG 方法实现了大尺度、参数丰富的仿真，并给出基态能量、磁化和相关性，与先前结果一致。
  • 在 η 接近 1 时，UUD 和 Y 相在大 η 和更大 S 时压缩，与自旋-5/2 系统观测到的更弱的 1/3 磁化台阶相一致。
Figure 2: Ground state phase diagrams of the monolayer TLXXZ model for $S=$ 1/2, 1, and 5/2, shown in panels (a-c), respectively. Circles with error bars are the calculated boundaries, while solid curves are guides to the eye. Thick black lines denote parity-breaking phase transitions. Arrows repres
Figure 2: Ground state phase diagrams of the monolayer TLXXZ model for $S=$ 1/2, 1, and 5/2, shown in panels (a-c), respectively. Circles with error bars are the calculated boundaries, while solid curves are guides to the eye. Thick black lines denote parity-breaking phase transitions. Arrows repres

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