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arXiv · 1408.3413

Anomalous diffusion and Griffiths effects near the many-body localization transition

Kartiek Agarwal·Sarang Gopalakrishnan·Michael Knap·Markus Mueller·Eugene Demler
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Abstract

We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) Local magnetization fluctuations relax subdiffusively; (ii) the a.c. conductivity vanishes near zero frequency as a power law; (iii) the distribution of resistances becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a Griffiths phase. We establish scaling relations between the associated exponents, using exact linear-response arguments as well as a phenomenological resistor-capacitor model.

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Kartiek Agarwal, Sarang Gopalakrishnan, Michael Knap, Markus Mueller, Eugene Demler. 2014-08-14. Anomalous diffusion and Griffiths effects near the many-body localization transition. https://doi.org/10.1103/physrevlett.114.160401

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