Excitations in strict 2-group higher gauge models of topological phases

TL;DR

This paper introduces an exactly solvable (3+1)d topological phase model based on strict 2-group data, revealing the algebraic structure of excitations and ground state degeneracy through a generalized tube algebra approach.

Contribution

It provides a lattice Hamiltonian realization of a higher gauge theory for topological phases and classifies elementary excitations using the tube algebra framework.

Findings

Classifies point-like and loop-like excitations in the model.

Derives the algebraic structure underlying excitations.

Shows ground state degeneracy equals the number of elementary loop-like excitations.

Abstract

We consider an exactly solvable model for topological phases in (3+1)d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a lattice Hamiltonian realisation of the Yetter homotopy 2-type topological quantum field theory. The Hamiltonian yields bulk flux and charge composite excitations that are either point-like or loop-like. Applying a generalised tube algebra approach, we reveal the algebraic structure underlying these excitations and derive the irreducible modules of this algebra, which in turn classify the elementary excitations of the model. As a further application of the tube algebra approach, we demonstrate that the ground state subspace of the three-torus is described by the central subalgebra of the tube algebra for torus boundary, demonstrating the ground state degeneracy is given by the number of elementary loop-like excitations.