Topological phases from higher gauge symmetry in 3+1 dimensions

Article

关键词: CROSSED MODULE;    FIELD-THEORY;    QUANTUM;    INVARIANTS;    DISCRETE;    LATTICE;    KNOTS;   

DOI  :  10.1103/PhysRevB.95.155118

来源: SCIE

【 摘 要 】

We propose an exactly solvable Hamiltonian for topological phases in 3 + 1 dimensions utilizing ideas from higher lattice gauge theory, where the gauge symmetry is given by a finite 2-group. We explicitly show that the model is a Hamiltonian realization of Yetter's homotopy 2-type topological quantum field theory whereby the ground-state projector of the model defined on the manifold M-3 is given by the partition function of the underlying topological quantum field theory for M-3 x [0,1]. We show that this result holds in any dimension and illustrate it by computing the ground state degeneracy for a selection of spatial manifolds and 2-groups. As an application we show that a subset of our model is dual to a class of Abelian Walker-Wang models describing 3 + 1 dimensional topological insulators.

【 授权许可】

Free