Symmetry Enrichment in Three-Dimensional Topological Phases
| Autor: | Zheng-Xin Liu, Peng Ye, Shang-Qiang Ning |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Physics
Quantum Physics Strongly Correlated Electrons (cond-mat.str-el) Statistical Mechanics (cond-mat.stat-mech) Unitarity FOS: Physical sciences Global symmetry Symmetry group Topology 01 natural sciences Deconfinement 010305 fluids & plasmas Mathematics::Logic Condensed Matter - Strongly Correlated Electrons Mathematics::Probability Gauge group Mathematics::Category Theory 0103 physical sciences Mathematics::Metric Geometry Gauge theory Quantum Physics (quant-ph) 010306 general physics U-1 Ground state Condensed Matter - Statistical Mechanics |
| Popis: | While two-dimensional symmetry-enriched topological phases ($\mathsf{SET}$s) have been studied intensively and systematically, three-dimensional ones are still open issues. We propose an algorithmic approach of imposing global symmetry $G_s$ on gauge theories (denoted by $\mathsf{GT}$) with gauge group $G_g$. The resulting symmetric gauge theories are dubbed "symmetry-enriched gauge theories" ($\mathsf{SEG}$), which may be served as low-energy effective theories of three-dimensional symmetric topological quantum spin liquids. We focus on $\mathsf{SEG}$s with gauge group $G_g=\mathbb{Z}_{N_1}\times\mathbb{Z}_{N_2}\times\cdots$ and on-site unitary symmetry group $G_s=\mathbb{Z}_{K_1}\times\mathbb{Z}_{K_2}\times\cdots$ or $G_s=\mathrm{U(1)}\times \mathbb{Z}_{K_1}\times\cdots$. Each $\mathsf{SEG}(G_g,G_s)$ is described in the path integral formalism associated with certain symmetry assignment. From the path-integral expression, we propose how to physically diagnose the ground state properties (i.e., $\mathsf{SET}$ orders) of $\mathsf{SEG}$s in experiments of charge-loop braidings (patterns of symmetry fractionalization) and the \emph{mixed} multi-loop braidings among deconfined loop excitations and confined symmetry fluxes. From these symmetry-enriched properties, one can obtain the map from $\mathsf{SEG}$s to $\mathsf{SET}$s. By giving full dynamics to background gauge fields, $\mathsf{SEG}$s may be eventually promoted to a set of new gauge theories (denoted by $\mathsf{GT}^*$). Based on their gauge groups, $\mathsf{GT}^*$s may be further regrouped into different classes each of which is labeled by a gauge group ${G}^*_g$. Finally, a web of gauge theories involving $\mathsf{GT}$, $\mathsf{SEG}$, $\mathsf{SET}$ and $\mathsf{GT}^*$ is achieved. We demonstrate the above symmetry-enrichment physics and the web of gauge theories through many concrete examples. 24 pages, 5 figures |
| Databáze: | OpenAIRE |
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