Stabilizing lattice gauge theories through simplified local pseudo generators

TL;DR

This paper introduces a method to stabilize gauge invariance in lattice gauge theories using simplified local pseudogenerators, reducing experimental complexity and enabling more faithful quantum simulations.

Contribution

The authors propose simplified local pseudogenerators that enforce gauge invariance effectively, avoiding complex multi-body implementations and maintaining gauge symmetry over significant timescales.

Findings

Emergent exact gauge theories up to polynomial and exponential timescales

Reduced experimental overhead by simplifying gauge-symmetry enforcement

Applicable to ultracold-atom quantum simulation platforms

Abstract

The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified \textit{local pseudogenerators} designed such that within the physical sector they act identically to the actual local generator. Dynamically, they give rise to emergent exact gauge theories up to timescales polynomial and even exponential in the protection strength. This obviates the need for implementing often complex multi-body full gauge symmetries, thereby further reducing experimental overhead in physical realizations. We showcase our method in the $\mathbb{Z}_2$ lattice gauge theory, and discuss experimental considerations for its realization in modern ultracold-atom setups.