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

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics

Background:

• Disordered quantum systems can exhibit many-body localization (MBL), a transition from ergodic to non-ergodic behavior.
• Understanding the metallic phase near the MBL transition is crucial for characterizing quantum dynamics in such systems.

Purpose of the Study:

• Investigate the high-temperature dynamics of the one-dimensional XXZ model in the delocalized phase near the MBL transition.
• Determine the physical properties governing this metallic phase and its relation to quantum criticality.

Main Methods:

• Analysis of the disordered, one-dimensional XXZ model at high temperatures.
• Focus on characterizing the metallic (delocalized) phase in proximity to the MBL transition.

Main Results:

• Observed subdiffusive relaxation of local magnetization fluctuations.
• Found that ac conductivity vanishes as a power law near zero frequency.
• Identified a broadening distribution of resistivities at low frequencies, approaching a power law.

Conclusions:

• The observed properties suggest the metallic phase near the MBL transition behaves as a quantum Griffiths phase.
• Established scaling relations between exponents based on spin-diffusion propagator scaling.
• A phenomenological resistor-capacitor model effectively captures the essential features of the system's dynamics.