Topological Order from a Cohomological and Higher Gauge Theory perspective

Abstract

In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which are not described by previous schemes of classification. In this paper we show that we can go beyond the $2$-gauge construction when considering chain complexes of abelian groups. Based on elements of homological algebra we are able to greatly simplify already known constructions for abelian theories under a single all encompassing framework. Furthermore, this formalism allows us to systematize the computation of the corresponding topological degeneracies of the ground states and establishes a connection between them and a known cohomology, which conveniently characterizes them with a suitable set of quantum numbers.

Cited by in corpus (8)

• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Higher-form symmetries and 3-group in axion electrodynamics
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• Topological non-linear $\sigma$-model, higher gauge theory, and a realization of all 3+1D topological orders for boson systems
• Fracton-like phases from subsystem symmetries
• Novel quantum phases on graphs using abelian gauge theory
• The low-energy TQFT of the generalized double semion model
• Non-Abelian fusion rules from Abelian systems with SPT phases and graph topological order