Toolbox for Abelian lattice gauge theories with synthetic matter

TL;DR

This paper introduces a class of 2D Abelian gauge theory models with rich phase diagrams, including exotic deconfined and gapless phases, and proposes experimental realization with ultracold atoms.

Contribution

It presents simple 2D models with emergent Abelian gauge theories, revealing complex phases and proposing experimental implementations.

Findings

Rich phase diagrams with deconfined and gapless phases

Emergence of additional symmetry leads to gapless phases in 2D

Feasible schemes for experimental realization with ultracold atoms

Abstract

Fundamental forces of Nature are described by field theories, also known as gauge theories, based on a local gauge invariance. The simplest of them is quantum electrodynamics (QED), which is an example of an Abelian gauge theory. Such theories describe the dynamics of massless photons and their coupling to matter. However, in two spatial dimension (2D) they are known to exhibit gapped phases at low temperature. In the realm of quantum spin systems, it remains a subject of considerable debate if their low energy physics can be described by emergent gauge degrees of freedom. Here we present a class of simple two-dimensional models that admit a low energy description in terms of an Abelian gauge theory. We find rich phase diagrams for these models comprising exotic deconfined phases and gapless phases - a rare example for 2D Abelian gauge theories. The counter-intuitive presence of gapless phases in 2D results from the emergence of additional symmetry in the models. Moreover, we propose schemes to realize our model with current experiments using ultracold bosonic atoms in optical lattices.