Dynamical generalization of Yetter's model based on a crossed module of discrete groups

Abstract

We construct a dynamical lattice model based on a crossed module of possibly non-abelian finite groups. Its degrees of freedom are defined on links and plaquettes, while gauge transformations are based on vertices and links of the underlying lattice. We specify the Hilbert space, define basic observables (including the Hamiltonian) and initiate a~discussion on the model's phase diagram. The constructed model generalizes, and in appropriate limits reduces to, topological theories with symmetries described by groups and crossed modules, lattice Yang-Mills theory and $2$-form electrodynamics. We conclude by reviewing classifying spaces of crossed modules, with an emphasis on the direct relation between their geometry and properties of gauge theories under consideration.

arXiv comment55 pages, 27 figures

References in corpus (21)

• Fault-tolerant quantum computation by anyons
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Classification of topological quantum matter with symmetries
• Generalized Global Symmetries
• String-net condensation: A physical mechanism for topological phases
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Dirac materials
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Coupling a QFT to a TQFT and Duality
• Superconductors are topologically ordered
• On 2-Group Global Symmetries and Their Anomalies
• An Invitation to Higher Gauge Theory
• Hamiltonian models for topological phases of matter in three spatial dimensions
• 4-Dimensional BF Theory as a Topological Quantum Field Theory
• Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics
• Higher lattices, discrete two-dimensional holonomy and topological phases in (3+1) D with higher gauge symmetry
• From gauge to higher gauge models of topological phases
• Topological phases from higher gauge symmetry in 3+1D
• Topological Higher Gauge Theory - from BF to BFCG theory
• Holonomy and parallel transport for Abelian gerbes

Cited by in corpus (1)

• Dynamics of a lattice 2-group gauge theory model