发表机构
Max Planck Institute for the Physics of Complex Systems; T.C.M. Group, Cavendish Laboratory, University of Cambridge（马克斯·普朗克复杂系统物理研究所; 剑桥大学卡文迪许实验室 T.C.M. 组）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在枫叶格和格子格上构建自旋模型，得到精确ℤ₂量子自旋液体，通过模拟和分析确定其拓扑序，建立涡旋与任意子对应关系并绘制拓扑相图。
AI 中文摘要
我们在五配位的枫叶格和格子格上构建具有键依赖各向异性相互作用的自旋模型，该模型产生类似于Kitaev蜂窝模型的精确ℤ₂量子自旋液体。我们通过通量区、陈数和拓扑激发来表征所得基态。利用副本交换量子蒙特卡罗模拟，我们发现在足够低的温度下规范通量有序，使得每个单位三角形具有±π/2通量，符号在整个系统中均匀；在感兴趣的参数空间内，每个单位六边形具有0通量，单位正方形具有π通量。我们绘制了每个模型的拓扑相图，其揭示了承载ℤ₂和伊辛拓扑序的参数区域，并推导了马约拉纳费米子质量项的解析表达式，该质量项消失表明这些相之间发生转变。我们进一步建立了单个涡旋（即通量激发）与二聚体极限中两种任意子之间的对应关系，克服了简并微扰理论在处理奇数长度基本 plaquette 时面临的障碍。有趣的是，我们发现枫叶模型的两个具有不同任意子种类分配的二聚体极限可在无涡旋区中平滑连接，但它们在某些双涡旋区中被费米子能隙闭合转变所分隔。
英文摘要
We construct spin models with bond-dependent anisotropic interactions on the penta-coordinated maple-leaf and trellis lattices, which yield exact $\mathbb{Z}_2$ quantum spin liquids akin to the Kitaev honeycomb model. We characterize the resulting ground states by their flux sectors, Chern numbers, and topological excitations. Using replica exchange quantum Monte Carlo simulations, we find that the gauge fluxes are ordered at sufficiently low temperatures such that every unit triangle has $\pm π/2$-flux, where the sign is uniform across the system, and every unit hexagon (square) has $0$-flux ($π$-flux) within the parameter space of interest. We map out the topological phase diagram for each model, which reveals parameter regimes hosting $\mathbb{Z}_2$ and Ising topological orders, and we derive an analytical expression for the mass term of the Majorana fermions, the vanishing of which indicates a transition between these phases. We further establish the correspondence between individual vortices (i.e., flux excitations) and two species of anyons in the dimer limit, overcoming the obstacle faced by degenerate perturbation theory in treating odd-length elementary plaquettes. Interestingly, we find that two dimer limits of the maple-leaf model with distinct assignments of anyon species can be smoothly connected to each other in the vortex-free sector, but they are separated by fermion-gap-closing transitions in certain two-vortex sectors.
Comments11+12 pages, 6+5 figures
