Gauge protection in non-abelian lattice gauge theories

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 (ED) 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 adjusted gauge theory with the same local gauge symmetry up to least a timescale $\propto \sqrt{V/{V}_{0}^{3}}$ . Thereafter, a renormalized gauge theory dominates up to a timescale ∝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 ED, 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 noisy intermediate-scale quantum (NISQ) devices.

Keywords

• lattice gauge theories
• gauge protection
• non-abelian gauge theories
• exact diagonalization