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Fixed Points of Wegner-Wilson Flows and Many-Body Localization
David Pekker1,2, Bryan K Clark3, Vadim Oganesyan4,5
1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
Physical Review Letters
|September 27, 2017
Summary
Many-body localization (MBL) prevents thermalization by generating local quantum numbers. A new algorithm reveals distinct distributions of these numbers across ergodic, MBL, and transition phases.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Statistical Mechanics
Background:
- Many-body localization (MBL) describes a phase of matter where thermalization fails.
- The dynamical generation of local quantum numbers is a key characteristic and potential driver of MBL.
- Understanding these conserved quantities is crucial for characterizing the MBL phase and its transitions.
Purpose of the Study:
- To develop a robust algorithm for computing local quantum numbers and their interactions.
- To investigate the distributions of these conserved quantities in different phases of matter.
- To identify the microscopic mechanisms underlying the breakdown of thermalization in MBL systems.
Main Methods:
- Formulation of a novel algorithm based on Wegner-Wilson flow (WWF) renormalization.
- Application of the algorithm to compute conserved quantities in many-body systems.
- Analysis of the fixed point distributions of these conserved quantities.
Main Results:
- The algorithm successfully computes local quantum numbers and their interactions.
- Distinct fixed point distributions were identified: Gaussian white-noise-like in the ergodic phase.
- A 1/f law was observed within the MBL phase, and scale-free distributions at the transition regime.
Conclusions:
- The developed WWF-based algorithm provides a robust method for studying MBL.
- The identified distributions offer insights into the nature of thermalization breakdown.
- This work elucidates the role of local quantum numbers in defining the MBL phase and its transitions.
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