Nonergodic dynamics in disorder-free potentials

TL;DR

This paper reviews nonergodic dynamics in disorder-free systems with a harmonic potential and tilt, highlighting the role of local tilt and domain structures in inhibiting transport and entanglement growth.

Contribution

It introduces an effective local tilt framework to explain nonergodic behavior in disorder-free potentials across various particle types.

Findings

Nonergodic features appear even with weak tilt.

Harmonic potential effects are mainly captured by local tilt.

Domain structures inhibit transport and influence entanglement.

Abstract

We review the dynamics of interacting particles in disorder-free potentials concentrating on a combination of a harmonic binding with a constant tilt. We show that a simple picture of an effective local tilt describes a variety of cases. Our examples include spinless fermions (as modeled by Heisenberg spin chain in a magnetic field), spinful fermions as well as bosons that enjoy a larger local on-site Hilbert space. We also discuss the domain-wall dynamics that reveals nonergodic features even for a relatively weak tilt as suggested by Doggen et. al. [arXiv:2012.13722]. By adding a harmonic potential on top of the static field we confirm that the surprizing regular dynamics is not entirely due to Hilbert space shuttering. It seems better explained by the inhibited transport within the domains of identically oriented spins. Once the spin-1/2 restrictions are lifted as, e.g., for bosons, the dynamics involve stronger entanglement generation. Again for domain wall melting, the effect of the harmonic potential is shown to lead mainly to an effective local tilt.