Gauge protection in non-Abelian lattice gauge theories

TL;DR

This paper demonstrates that gauge invariance in non-Abelian lattice gauge theories can be reliably protected using energy-penalty schemes, ensuring the stability of the gauge sector and suppressing violations in quantum simulations.

Contribution

It introduces a volume-independent gauge protection scheme for non-Abelian theories, showing how to control gauge violations with fewer experimental resources.

Findings

Gauge violations are suppressed with sufficiently large protection strength.

An adjusted gauge theory emerges with volume-independent protection.

Single-body protection terms effectively suppress violations over accessible timescales.

Abstract

Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-Abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization that non-Abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength $V$, which when sufficiently large leads to the emergence of an \textit{adjusted} gauge theory with the same local gauge symmetry up to least a timescale $\propto\sqrt{V/V_0^3}$. Thereafter, a \textit{renormalized} gauge theory dominates up to a timescale $\propto\exp(V/V_0)/V_0$ with $V_0$ a volume-independent energy factor, similar to the case of faulty Abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in exact diagonalization, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and NISQ devices.