Reliability of lattice gauge theories in the thermodynamic limit
Abstract
Although gauge invariance is a postulate in fundamental theories of nature such as quantum electrodynamics, in quantumsimulation implementations of gauge theories it is compromised by experimental imperfections. In a recent work [Halimeh and Hauke, \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.030503}{Phys. Rev. Lett. \textbf{125}, 030503 (2020)}], it has been shown in finitesize spin$1/2$ quantum link lattice gauge theories that upon introducing an energypenalty term of sufficiently large strength $V$, unitary gaugebreaking errors at strength $\lambda$ are suppressed $\propto\lambda^2/V^2$ up to all accessible evolution times. Here, we show numerically that this result extends to quantum link models in the thermodynamic limit and with larger spin$S$. As we show analytically, the dynamics at short times is described by an \textit{adjusted} gauge theory up to a timescale that is at earliest $\tau_\text{adj}\propto\sqrt{V/V_0^3}$, with $V_0$ an energy factor. Moreover, our analytics predicts that a renormalized gauge theory dominates at intermediate times up to a timescale $\tau_\text{ren}\propto\exp(V/V_0)/V_0$. In both emergent gauge theories, $V$ is volumeindependent and scales at worst $\sim S^2$. Furthermore, we numerically demonstrate that robust gauge invariance is also retained through a singlebody gaugeprotection term, which is experimentally straightforward to implement in ultracoldatom setups and NISQ devices.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 DOI:
 10.48550/arXiv.2104.07040
 arXiv:
 arXiv:2104.07040
 Bibcode:
 2021arXiv210407040V
 Keywords:

 Condensed Matter  Quantum Gases;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 Quantum Physics
 EPrint:
 journal article, 17 pages, 15 figures