Low-frequency conductivity in many-body localized systems

TL;DR

This paper investigates the low-frequency a.c. conductivity in many-body localized systems, revealing a power-law behavior with an exponent that varies across the phase transition, supported by numerical evidence and experimental implications.

Contribution

It identifies two distinct mechanisms for the power-law conductivity in MBL systems and characterizes how the exponent evolves near the phase transition.

Findings

Conductivity follows a power law: σ(ω) ~ ω^α.

Exponent α approaches 1 at the transition and 2 deep in the localized phase.

Numerical evidence supports the proposed mechanisms and power-law behavior.

Abstract

We argue that the a.c. conductivity $\sigma(\omega)$ in the many-body localized phase is a power law of frequency $\omega$ at low frequency: specifically, $\sigma(\omega) \sim \omega^\alpha$ with the exponent $\alpha$ approaching 1 at the phase transition to the thermal phase, and asymptoting to 2 deep in the localized phase. We identify two separate mechanisms giving rise to this power law: deep in the localized phase, the conductivity is dominated by rare resonant pairs of configurations; close to the transition, the dominant contributions are rare regions that are locally critical or in the thermal phase. We present numerical evidence supporting these claims, and discuss how these power laws can also be seen through polarization-decay measurements in ultracold atomic systems.