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.

Gauge protection in non-abelian lattice gauge theories / Halimeh, Jad C.; Lang, Haifeng; Hauke, Philipp. - In: NEW JOURNAL OF PHYSICS. - ISSN 1367-2630. - 24:3(2022), p. 033015. [10.1088/1367-2630/ac5564]

Gauge protection in non-abelian lattice gauge theories

Lang, Haifeng;Hauke, Philipp
2022-01-01

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.
2022
3
Halimeh, Jad C.; Lang, Haifeng; Hauke, Philipp
Gauge protection in non-abelian lattice gauge theories / Halimeh, Jad C.; Lang, Haifeng; Hauke, Philipp. - In: NEW JOURNAL OF PHYSICS. - ISSN 1367-2630. - 24:3(2022), p. 033015. [10.1088/1367-2630/ac5564]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/399890
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