Reliability of lattice gauge theories

TL;DR

This paper investigates the robustness of lattice gauge theories in quantum simulators, showing that gauge violations grow slowly and can be suppressed, ensuring reliable simulation despite imperfections.

Contribution

It provides a theoretical and numerical analysis demonstrating how gauge violations evolve and can be controlled in quantum simulators of lattice gauge theories.

Findings

Gauge violations grow perturbatively at short times

Long-time proliferation of violations can be suppressed

Energetic penalties effectively protect gauge invariance

Abstract

Currently, there are intense experimental efforts to realize lattice gauge theories in quantum simulators. Except for specific models, however, practical quantum simulators can never be fine-tuned to perfect local gauge invariance. There is thus a strong need for a rigorous understanding of gauge-invariance violation and how to reliably protect against it. As we show through analytic and numerical evidence, in the presence of a gauge invariance-breaking term the gauge violation accumulates only perturbatively at short times before proliferating only at very long times. This proliferation can be suppressed up to infinite times by energetically penalizing processes that drive the dynamics away from the initial gauge-invariant sector. Our results provide a theoretical basis that highlights a surprising robustness of gauge-theory quantum simulators.