Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition

作者：Agarwal, Kartiek^*; Gopalakrishnan, Sarang; Knap, Michael; Mueller, Markus; Demler, Eugene

来源：Physical Review Letters, 2015, 114(16): 160401.

DOI：10.1103/PhysRevLett.114.160401

• METAL-INSULATOR-TRANSITION
• ANDERSON LOCALIZATION
• DISORDERED-SYSTEMS
• OPTICAL LATTICE
• CONDUCTION
• IMPURITY
• STATES
• CHAIN
• PHASE

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 ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities 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 quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.

• 出版日期2015-4-23