Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case

Abstract

In this work, the second paper of this series, we study the 2+1d version of a Hamiltonian model for topological phases based on higher lattice gauge theory. We construct the ribbon operators that produce the point-like excitations. These ribbon operators are used to find the braiding properties and topological charge carried by the point-like excitations. The model also hosts loop-like excitations, which are produced by membrane operators. By considering a change of basis, we show that, in certain cases, some loop-like excitations represent domain walls between patches corresponding to different symmetry-related ground states, and we find this symmetry. We also map the higher lattice gauge theory Hamiltonian to the symmetry enriched string-net model for symmetry enriched topological phases (SETs) described by Heinrich, Burnell, Fidkowski and Levin [Phys. Rev. B, 94, 235136 (2016)], again in a subset of cases.

60 pages + 100 pages of Supplementary Material, 50 figures + 50 figures in Supplementary Material, v2: expanded Section II, various minor changes for publication

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Cited by in corpus (4)

• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases III: the (3+1)-Dimensional Case
• Finite 2-group gauge theory and its 3+1D lattice realization