Large-Scale $2+1$D $\mathrm{U}(1)$ Gauge Theory with Dynamical Matter in a Cold-Atom Quantum Simulator

TL;DR

This paper proposes a feasible method to realize a large-scale 2+1D U(1) gauge theory with dynamical matter in a cold-atom quantum simulator, enabling exploration of high-energy phenomena in synthetic quantum matter.

Contribution

It introduces a full mapping of the gauge theory onto bosonic basis and demonstrates stabilization using an emergent gauge protection term in a cold-atom setup.

Findings

Numerical benchmarks confirm high fidelity of the gauge theory realization.

The proposed setup requires only moderate resources available in current cold-atom experiments.

The work advances quantum simulation of higher-dimensional gauge theories.

Abstract

A major driver of quantum-simulator technology is the prospect of probing high-energy phenomena in synthetic quantum matter setups at a high level of control and tunability. Here, we propose an experimentally feasible realization of a large-scale $2+1$D $\mathrm{U}(1)$ gauge theory with dynamical matter and gauge fields in a cold-atom quantum simulator with spinless bosons. We present the full mapping of the corresponding Gauss's law onto the bosonic computational basis. We then show that the target gauge theory can be faithfully realized and stabilized by an emergent gauge protection term in a two-dimensional single-species Bose--Hubbard optical Lieb superlattice with two spatial periods along either direction, thereby requiring only moderate experimental resources already available in current cold-atom setups. Using infinite matrix product states, we calculate numerical benchmarks for adiabatic sweeps and global quench dynamics that further confirm the fidelity of the mapping. Our work brings quantum simulators of gauge theories a significant step forward in terms of investigating particle physics in higher spatial dimensions, and is readily implementable in existing cold-atom platforms.