A Classification of (2+1)D Topological Phases with Symmetries

2018/01/04 by Tian Lan, Lan, Tian
Physics and Astronomy · #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Scientific Research and Discoveries #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.1801.01210

openalex publication_date 2018/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This thesis aims at concluding the classification results for topological phases with symmetry in 2+1 dimensions. The main result is that topological phases are classified by a triple of unitary braided fusion categories \mathcal E⊂\mathcal C⊂\mathcal M plus the chiral central charge c. Here \mathcal E is a symmetric fusion category, \mathcal E=Rep(G) for boson systems or \mathcal E=sRep(G^f) for fermion systems, consisting of the representations of the symmetry group and describing the local excitations with symmetry; \mathcal C is the category of all the quasiparticle excitations in the bulk, containing \mathcal E as its Müger center; \mathcal M is a minimal modular extension of \mathcal C, that also includes the gauged symmetry defects. We also study the stacking of topological phases with symmetry and two types of anyon condensations based on such classification.

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