Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications

TL;DR

This paper explores the physical constructions and boundary properties of symmetry protected topological (SPT) phases involving higher symmetries, especially 1-form symmetries, across dimensions 1d to 4d, with implications for condensed matter systems.

Contribution

It introduces new insights into the boundary states of higher-symmetry SPT phases and their relation to anomaly diagnosis and condensed matter models like quantum dimer models.

Findings

3d boundary states can be gapless photon phases or gapped topological orders with 1-form symmetry charges

Connection established between higher-symmetry SPT states and quantum dimer models

Analysis of anomaly diagnostics for 3d states of matter

Abstract

We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d boundary state of 4d SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries, namely the loop excitations of these topological orders carry nontrivial 1-form symmetry charges. This study also serves the purpose of diagnosing anomaly of 3d states of matter. Connection between SPT states with 1-form symmetries and condensed matter systems such as quantum dimer models at one lower dimension will also be discussed. Whether a quantum dimer model can have a trivial gapped phase or not depends on the nature of its corresponding bulk state in one higher dimension.