Abstract
We argue that the ac conductivity in the many-body localized phase is a power law of frequency at low frequency: specifically, with the exponent 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.
- Received 5 May 2015
- Revised 22 August 2015
DOI:https://doi.org/10.1103/PhysRevB.92.104202
©2015 American Physical Society