Symmetry-protected topological phases in lattice gauge theories: topological QED$_2$

TL;DR

This paper demonstrates the existence of symmetry-protected topological phases in a (1+1)-dimensional lattice gauge theory, specifically a variant of QED$_2$, revealing new topological phenomena in high-energy physics.

Contribution

It introduces a new topological phase in a gauge theory, combining bosonization and DMRG methods, and proposes experimental realization in cold atom systems.

Findings

Identification of SPT phases in a lattice gauge theory

Topological contribution to the vacuum θ angle

Proposed experimental realization in optical lattices

Abstract

The interplay of symmetry, topology, and many-body effects in the classification of possible phases of matter poses a formidable challenge that is attracting great attention in condensed-matter physics. Such many-body effects are typically induced by inter-particle interactions involving an action at a distance, such as the Coulomb interaction between electrons in a symmetry-protected topological (SPT) phase. In this work, we show that similar phenomena also appear in high-energy physics, where inter-particle interactions are mediated by gauge bosons, and constrained by a local gauge symmetry. We introduce a variant of the so-called Schwinger model, which describes quantum electrodynamics in (1+1) dimensions (QED$_2$), and show that it can host SPT phases with a topological contribution to the vacuum {\theta} angle, which leads to a new type of topological QED$_2.$ We use bosonization and density-matrix renormalization group techniques to study its rich phase diagram in great detail, and present a scheme for its realization in experiments of ultra-cold atoms in optical lattices.