Gauge protection in non-abelian lattice gauge theories

Year: 2022

Authors: Halimeh J.C.; Lang H., Hauke P.

Autors Affiliation: Univ Trento, INO CNR BEC Ctr, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dept Phys, Via Sommar 14, I-38123 Trento, Italy; Heidelberg Univ, Theoret Chem, Inst Phys Chem, Neuenheimer Feld 229, D-69120 Heidelberg, Germany

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 proportional to root V / V-0(3). Thereafter, a renormalized gauge theory dominates up to a timescale proportional to 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.


Volume: 24 (3)      Pages from: 033015-1  to: 033015-14

More Information: The authors are grateful to Debasish Banerjee, Marcello Dalmonte, Federica M Surace, and Maarten Van Damme for valuable comments. This work is part of and supported by Provincia Autonoma di Trento, the ERC Starting Grant StrEnQTh (project ID 804305), the Google Research Scholar Award ProGauge, and Q@TN-Quantum Science and Technology in Trento.
KeyWords: lattice gauge theories; gauge protection; non-abelian gauge theories; exact diagonalization
DOI: 10.1088/1367-2630/ac5564