Staircase prethermalization and gauge stabilization in lattice gauge theories

The dynamics of lattice gauge theories is characterized by an abundance of local symmetry constraints. Although errors that break gauge symmetry appear naturally in modern quantum simulators, their influence on the gauge-theory dynamics is insufficiently investigated. In this talk, we show that a small gauge breaking of strength λ 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 λ^-L/2, indicating 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. We then discuss experimentally feasible gauge protection schemes based on energy constraints for the stabilization of gauge invariance in the presence of such errors, showing numerically and analytically the emergence of exact gauge theories up to timescales polynomial and even exponential in a volume-independent protection strength. We showcase such schemes in an experimental realization of a U(1) lattice gauge theory on a 71-site Bose--Hubbard quantum simulator.

Note to organizers: I would be very much interested in upgrading to an invited talk.