Reliability of lattice gauge theories in the thermodynamic limit br

Year: 2023

Authors: Van Damme M., Lang HF., Hauke P., Halimeh JC.

Autors Affiliation: Univ Ghent, Dept Phys & Astron, Krijgslaan 281, B-9000 Ghent, Belgium; Univ Trento, INO CNR BEC Ctr & Dept Phys, I-38123 Trento, Italy; Heidelberg Univ, Inst Phys Chem, Theoret Chem, Neuenheimer Feld 229, D-69120 Heidelberg, Germany.

Abstract: Although gauge invariance is a postulate in fundamental theories of nature such as quantum electrodynamics,in quantum-simulation implementations of gauge theories it is compromised by experimental imperfections. In arecent paper [Halimeh and Hauke,Phys.Rev.Lett.125, 030503 (2020)], it has been shown in finite-size spin-1/2quantum link lattice gauge theories that upon introducing an energy-penalty term of sufficiently large strengthV, unitary gauge-breaking errors at strength lambda are suppressed proportional to lambda 2/V2up to all accessible evolution times.Here, we show numerically that this result extends to quantum link models in the thermodynamic limit and withlarger spinS. As we show analytically, the dynamics at short times is described by anadjustedgauge theoryup to a timescale that is at earliest tau adj proportional to root V/V30, withV0an energy factor. Moreover, our analytics predictsthat a renormalized gauge theory dominates at intermediate times up to a timescale tau ren proportional to exp(V/V0)/V0.Inboth emergent gauge theories,Vis volume independent and scales at worst similar to S2. Furthermore, we numericallydemonstrate that robust gauge invariance is also retained through a single-body gauge-protection term, which isexperimentally straightforward to implement in ultracold-atom setups and NISQ device

Journal/Review: PHYSICAL REVIEW B

Volume: 107 (3)      Pages from: 35153-1  to: 35153-15

More Information: M.V.D. and H.L. contributed equally to this work. J.C.H. is grateful to Fred Jendrzejewski, Guoxian Su, and Bing Yang for discussions related to experimental aspects of this work. We acknowledge support by Provincia Autonoma di Trento, the ERC Starting Grant StrEnQTh (Project-ID 804305), Q@TN — Quantum Science and Technology in Trento, ERC Grants No. 715861 (ERQUAF) and No. 647905 (QUTE), and from Research Foundation Flanders (FWO) via Grant No. GOE1520N.
KeyWords: Many-body Localization; Quantum Simulation; Dynamics; Prethermalization; Invariance
DOI: 10.1103/PhysRevB.107.035153

Citations: 2
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