Critical localization with Van der Waals interactions

TL;DR

This paper explores a novel critically localized many-body regime in disordered quantum systems with long-range Van der Waals interactions, highlighting its stability, phenomenology, and experimental realizations.

Contribution

It introduces the concept of a critically many body localized regime stable at low perturbation orders in systems with $1/r^{2d}$ interactions, and discusses its experimental relevance.

Findings

Localization remains stable at low orders of perturbation theory.

Distinctive signatures in entanglement, charge statistics, noise, and transport.

Avalanche phenomena limit the lifetime of the critical MBL regime.

Abstract

I discuss the quantum dynamics of strongly disordered quantum systems with critically long range interactions, decaying as $1/r^{2d}$ in $d$ spatial dimensions. I argue that, contrary to expectations, localization in such systems is stable at low orders in perturbation theory, giving rise to an unusual `critically many body localized regime.' I discuss the phenomenology of this critical MBL regime, which includes distinctive signatures in entanglement, charge statistics, noise, and transport. Experimentally, such a critically localized regime can be realized in three dimensional systems with Van der Waals interactions, such as Rydberg atoms, and in one dimensional systems with $1/r^2$ interactions, such as trapped ions. I estimate timescales on which high order perturbative and non-perturbative (avalanche) phenomena may destabilize this critically MBL regime, and conclude that the avalanche sets the limiting timescale, in the limit of strong disorder / weak interactions.