Exactly solvable models for U(1) symmetry-enriched topological phases

Abstract

We propose a general construction of commuting projector lattice models for 2D and 3D topological phases enriched by U(1) symmetry, with finite-dimensional Hilbert space per site. The construction starts from a commuting projector model of the topological phase and decorates U(1) charges to the state space in a consistent manner. We show that all 2D U(1) symmetry-enriched topological phases which allow gapped boundary without breaking symmetry, can be realized through our construction. We also construct a large class of 3D topological phases with U(1) symmetry fractionalized on particles or loop excitations.

16 pages, 2 figures

References in corpus (4)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• A classification of symmetry enriched topological phases with exactly solvable models
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Twisted gauge theories in 3D Walker-Wang models

Cited by in corpus (11)

• Lecture Notes on Generalized Symmetries and Applications
• Boundary and domain wall theories of 2d generalized quantum double model
• Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians
• Classification of symmetry-enriched topological quantum spin liquids
• Exactly solvable lattice models for interacting electronic insulators in two dimensions
• $U(1)$ symmetry-enriched toric code
• (3+1)D path integral state sums on curved U(1) bundles and U(1) anomalies of (2+1)D topological phases
• Electric-magnetic duality and ${\mathbb{Z}}_2$ symmetry enriched Abelian lattice gauge theory
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly
• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization