# Staircase Prethermalization and Constrained Dynamics in Lattice Gauge Theories

Date
Apr 21, 2021
Event
Leeds-Loughborough-Nottingham Nonequilibrium Seminar

### Abstract

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. In this talk, we show that a small gauge breaking of strength $\lambda$ induces a staircase of long-lived prethermal plateaus. The number of prethermal plateaus increases with the number of matter fields $L$, with the last plateau being reached at a timescale $\lambda^{−L/2}$, showing an intimate relation of the concomitant slowing down of dynamics with the number of local gauge constraints. 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. 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. From a phenomenological perspective, our work shows how prethermal behavior is significantly enriched in models with slight breaking of local gauge invariance relative to their counterparts where a global symmetry is broken.

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