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arXiv:2004.07254

Origin of staircase prethermalization in lattice gauge theories

Jad C. Halimeh, Philipp Hauke

Published Jan 1, 2020• 1 citation
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Abstract

Quantum many-body systems with exact local gauge symmetries exhibit rich out-of-equilibrium physics such as constrained dynamics and disorder-free localization. In a joint submission [J. C. Halimeh and P. Hauke, arXiv:2004.07248], we present evidence of extit{staircase prethermalization} in a $mathrm{Z}_2$ lattice gauge theory subjected to a small breaking of gauge invariance. Here, we consolidate this finding and the associated emergent nonperturbative timescales analytically and numerically. By means of a Magnus expansion, we demonstrate how exact resonances between different gauge-invariant supersectors are the main reason behind the emergence of staircase prethermalization. Furthermore, we showcase the robustness of our conclusions against various initial conditions including different system sizes, matter fillings, and gauge-invariance sectors, in addition to various boundary conditions, such as different maximal on-site matter occupations. We also elaborate on how our conclusions are unique to local-symmetry models and why they break down in the case of global-symmetry breaking. We moreover extend our results to $mathrm{U}(1)$ lattice gauge theories, illustrating the generality of our findings. Our work offers an analytic footing into the constrained dynamics of lattice gauge theories and provides proof of a certain intrinsic robustness of gauge-theory dynamics to errors in experimental settings.

DOI
10.48550/arxiv.2004.07254

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Quantum many-body systems with exact local gauge symmetries exhibit rich out-of-equilibrium physics such as constrained dynamics and disorder-free localization. In a joint submission [J. C. Halimeh and P. Hauke, arXiv:2004.07248], we present evidence of extit{staircase prethermalization} in a mathrmZ2mathrm{Z}_2mathrmZ2​ lattice gauge theory subjected to a small breaking of gauge invariance. Here, we consolidate this finding and the associated emergent nonperturbative timescales analytically and numerically. By means of a Magnus expansion, we demonstrate how exact resonances between different gauge-invariant supersectors are the main reason behind the emergence of staircase prethermalization. Furthermore, we showcase the robustness of our conclusions against various initial conditions including different system sizes, matter fillings, and gauge-invariance sectors, in addition to various boundary conditions, such as different maximal on-site matter occupations. We also elaborate on how our conclusions are unique to local-symmetry models and why they break down in the case of global-symmetry breaking. We moreover extend our results to mathrmU(1)mathrm{U}(1)mathrmU(1) lattice gauge theories, illustrating the generality of our findings. Our work offers an analytic footing into the constrained dynamics of lattice gauge theories and provides proof of a certain intrinsic robustness of gauge-theory dynamics to errors in experimental settings.
The dynamics of lattice gauge theories is characterized by an abundance of local symmetry constraints. Although errors that break gauge symmetry appear naturally in NISQ-era quantum simulators, their influence on the gauge-theory dynamics is insufficiently investigated. As we show, a small gauge breaking of strength λλλ induces a staircase of long-lived prethermal plateaus. The number of prethermal plateaus increases with the number of matter fields LLL, with the last plateau being reached at a timescale λ−L/2λ^{-L/2}λ−L/2, showing an intimate relation of the concomitant slowing down of dynamics with the number of local gauge constraints. Our results bode well for NISQ quantum devices, as they indicate that the proliferation timescale of gauge-invariance violation is counterintuitively delayed exponentially in system size.
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Prethermal gauge structure and surface growth in Z2\mathbb{Z}_2Z2​ lattice gauge theories
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Disorder-free localization is a recently discovered phenomenon of nonergodicity that can emerge in quantum many-body systems hosting gauge symmetries when the initial state is prepared in a superposition of gauge superselection sectors.Thermalization is then prevented up to all accessible evolution times despite the model being nonintegrable and translation invariant.In a recent work [Halimeh et al., arXiv:2111.02427(2021)], it has been shown that terms linear in the gauge-symmetry generator stabilize disorder-free localization in U(1) gauge theories against gauge errors that couple different superselection sectors.Here, we show in the case of Z 2 gauge theories that disorder-free localization can not only be stabilized, but also enhanced by the addition of translation-invariant terms linear in a local Z 2 pseudogenerator that acts identically to the full generator in a single superselection sector, but not necessarily outside of it.We show analytically and numerically how this leads through the quantum Zeno effect to the dynamical emergence of a renormalized gauge theory with an enhanced local symmetry, which contains the Z 2 gauge symmetry of the ideal model, associated with the Z 2 pseudogenerator.The resulting proliferation of superselection sectors due to this dynamically emergent gauge theory creates an effective disorder greater than that in the original model, thereby enhancing disorder-free localization.We demonstrate the experimental feasibility of the Z 2 pseudogenerator by providing a detailed readily implementable experimental proposal for the observation of disorder-free localization in a Rydberg setup.
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Localization due to the presence of disorder has proven crucial for our current understanding of relaxation in isolated quantum systems. The many-body localized phase constitutes a robust alternative to the thermalization of complex interacting systems, but recently the importance of disorder has been brought into question. A number of disorder-free localization mechanisms have been put forward connected to local symmetries of lattice gauge theories. Here, starting from translationally invariant (1+1)(1+1)(1+1)-dimensional quantum electrodynamics, we modify the dynamics of the gauge field which allows us to construct a lattice model with a UUU(1) local gauge symmetry revealing a mechanism of disorder-free localization. We consider two different discretizations of the continuum model resulting in a free-fermion soluble model in one case and an interacting model in the other. We diagnose the localization of our translationally invariant model in the far-from-equilibrium dynamics following a global quantum quench.