How does a locally constrained quantum system localize?

TL;DR

This paper demonstrates that many-body localization can occur in locally constrained quantum systems, revealing new mechanisms and conditions for localization versus thermalization, with implications for Rydberg atom experiments.

Contribution

It shows full MBL stability in disordered constrained spin chains and uncovers a new resonance-based localization mechanism at strong transverse disorder.

Findings

Full MBL is stable at strong $z$-field disorder.

A new localization mechanism via resonance at strong transverse disorder.

Transition between localized and thermal phases is discontinuous with sample variability.

Abstract

At low energy, the dynamics of excitations of many physical systems are locally constrained. Examples include frustrated anti-ferromagnets, fractional quantum Hall fluids and Rydberg atoms in the blockaded regime. Can such locally constrained systems be fully many-body localized (MBL)? In this article, we answer this question affirmatively and elucidate the structure of the accompanying quasi-local integrals of motion. By studying disordered spin chains subject to a projection constraint in the $z$-direction, we show that full MBL is stable at strong $z$-field disorder and identify a new mechanism of localization through resonance at strong transverse disorder. However MBL is not guaranteed; the constraints can `frustrate' the tendency of the spins to align with the transverse fields and lead to full thermalization or criticality. We further provide evidence that the transition is discontinuous in local observables with large sample-to-sample variations. Our study has direct consequences for current quench experiments in Rydberg atomic chains.