论文标题
Vison Transport in $ \ Mathbb {Z} _2 $拓扑订购的状态的浆果阶段
Berry Phases of Vison Transport in $\mathbb{Z}_2$ Topologically Ordered States from Exact Fermion-Flux Lattice Dualities
论文作者
论文摘要
我们开发了从2D旋转2D晶格的所有状态和运营商的确切图表，$ 1/2 $，将其与相互半统计互动的晶格和玻色子的晶格中，超出了$ \ Mathbb {Z} _2 _2 $ lattice lattice Caguge的先前双重性，因为它不依赖于当地保护法和捕获的范围，并捕获了平衡的动作。立足。这张地图允许明确计算浆液阶段，以在大量的对称性富含拓扑的状态中运输通量，并以$ \ mathbb {z} _2 _2 $ s $ gouge田地出现，包括手性，包括手性，非手质，阿比亚人或非阿贝尔人的范围均无动机，并且可以诱使幻想的范围，并且既不触诊又有诱人的行为，并且既不触及了分散。因此，计算此类Vison阶段的数值复杂性将其降低到自由阵容汉密尔顿人的基础状态的计算重叠。除其他结果外，我们从数值上建立了富含翻译的统一级订购状态中的主要载体磁通激发的条件。
We develop an exact map of all states and operators from 2D lattices of spins-$1/2$ into lattices of fermions and bosons with mutual semionic statistical interaction that goes beyond previous dualities of $\mathbb{Z}_2$ lattice gauge theories because it does not rely on imposing local conservation laws and captures the motion of ``charges'' and ``fluxes'' on equal footing. This map allows to explicitly compute the Berry phases for the transport of fluxes in a large class of symmetry enriched topologically ordered states with emergent $\mathbb{Z}_2$ gauge fields that includes chiral, non-chiral, abelian or non-abelian, that can be perturbatively connected to models where the visons are static and the emergent fermionic spinons have a non-interacting dispersion. The numerical complexity of computing such vison phases reduces therefore to computing overlaps of ground states of free-fermion Hamiltonians. Among other results, we establish numerically the conditions under which the Majorana-carrying flux excitation in Ising-Topologically-Ordered states enriched by translations acquires $0$ or $π$ phase when moving around a single plaquette.
