Detecting Many-Body-Localization Length with Cold Atoms

TL;DR

This paper proposes experimental protocols using ultracold atoms in optical lattices to measure the many-body localization length and criticality, providing a new way to study phase transitions in quantum systems.

Contribution

It introduces a novel dynamical method to determine the MBL transition point and critical exponent through density profile measurements after a local quench.

Findings

Localization length diverges at the MBL transition with increasing system size.

The transition point matches previous diagnostics from exact diagonalization.

Evidence suggests violation of the Harris-Chayes bound for MBL criticality.

Abstract

Considering ultracold atoms in optical lattices, we propose experimental protocols to study many-body localization (MBL) length and criticality in quench dynamics. Through numerical simulations with exact diagonalization, we show that in the MBL phase the perturbed density profile following a local quench remains exponentially localized in post-quench dynamics. The size of this density profile after long-time-dynamics defines a localization length, which tends to diverge at the MBL-to-ergodic transition as we increase the system size. The determined localization transition point agrees with previous exact diagonalization calculations using other diagnostics. Our numerical results provide evidence for violation of Harris-Chayes bound for the MBL criticality. The critical exponent $\nu$ can be extracted from our proposed dynamical procedure, which can then be used directly in experiments to determine whether the Harris-Chayes-bound holds for the MBL transition. These proposed protocols to detect localization criticality are justified by benchmarking to the well-established results for the non-interacting 3D Anderson localization.