Fixed points of Wegner-Wilson flows and many-body localization

TL;DR

This paper introduces a Wegner Wilson flow-based algorithm to identify conserved quantities in many-body localization, revealing distinct fixed point distributions across phases.

Contribution

It develops a robust renormalization algorithm to compute local conserved quantities and their distributions in MBL systems, providing new insights into phase transition characteristics.

Findings

Flat 'white noise' distribution in ergodic phase

'1/f' distribution in MBL phase

Scale-free distributions at transition regime

Abstract

Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization. Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself. We formulate a robust algorithm, based on Wegner Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions. We present evidence for the existence of distinct fixed point distributions of the latter: a flat "white noise" distribution in the ergodic phase, a "1/f" law inside the MBL phase, and scale-free distributions in the transition regime.