Low-frequency conductivity in many-body localized systems
Abstract
We argue that the ac conductivity σ (ω ) in the many-body localized phase is a power law of frequency ω at low frequency: specifically, σ (ω ) ∼ωα with the exponent α 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.
- Publication:
-
Physical Review B
- Pub Date:
- September 2015
- DOI:
- 10.1103/PhysRevB.92.104202
- arXiv:
- arXiv:1502.07712
- Bibcode:
- 2015PhRvB..92j4202G
- Keywords:
-
- 72.15.Rn;
- 71.30.+h;
- 05.60.Gg;
- Localization effects;
- Metal-insulator transitions and other electronic transitions;
- Quantum transport;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Quantum Gases;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 10 pages, 6 figures