Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains

TL;DR

This paper investigates non-ergodic behavior in tilted Fermi-Hubbard chains, revealing long-lived initial states due to kinetic constraints, supported by experiments, simulations, and analytical insights.

Contribution

It provides the first comprehensive experimental and theoretical analysis of non-ergodicity caused by kinetic constraints in the tilted Fermi-Hubbard model.

Findings

Long-lived charge-density wave states observed experimentally.

Numerical simulations match experimental results.

Analytical calculations attribute behavior to emergent kinetic constraints.

Abstract

The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.