Gauge protection in non-abelian lattice gauge theories
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 the...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
11 March 2022
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| In: |
New journal of physics
Year: 2022, Volume: 24, Issue: 3, Pages: 1-14 |
| ISSN: | 1367-2630 |
| DOI: | 10.1088/1367-2630/ac5564 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1088/1367-2630/ac5564
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| Author Notes: | Jad C. Halimeh, Haifeng Lang, Philipp Hauke |
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| 520 | |a 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 . 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. | ||
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