Analytically solvable renormalization group for the many-body localization transition

TL;DR

This paper presents an exactly solvable renormalization group model for the many-body localization transition in one dimension, revealing a Kosterlitz-Thouless universality class with multifractal properties.

Contribution

It introduces a novel, analytically solvable RG framework for MBL transition, highlighting the role of asymmetry and rare thermal inclusions.

Findings

Identifies a localized critical point with power-law thermal inclusions.

Shows the typical inclusion size remains finite at transition.

Proposes a two-parameter scaling theory in the Kosterlitz-Thouless class.

Abstract

We introduce a simple, exactly solvable strong-randomness renormalization group (RG) model for the many-body localization (MBL) transition in one dimension. Our approach relies on a family of RG flows parametrized by the asymmetry between thermal and localized phases. We identify the physical MBL transition in the limit of maximal asymmetry, reflecting the instability of MBL against rare thermal inclusions. We find a critical point that is localized with power-law distributed thermal inclusions. The typical size of critical inclusions remains finite at the transition, while the average size is logarithmically diverging. We propose a two-parameter scaling theory for the many-body localization transition that falls into the Kosterlitz-Thouless universality class, with the MBL phase corresponding to a stable line of fixed points with multifractal behavior.