Many-body localization phase transition: A simplified strong-randomness approximate renormalization group

TL;DR

This paper introduces a simplified strong-randomness RG approach to model the MBL phase transition in disordered 1D systems, providing analytical insights and critical exponents consistent with previous numerical findings.

Contribution

It develops an analytically formulable RG method that captures key features of the MBL transition, including critical exponents and fractal Griffiths regions, serving as a foundational approximation.

Findings

Critical exponents obtained numerically

Fractal nature of Griffiths regions identified

RG reproduces qualitative features of MBL transition

Abstract

We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically, and the critical fixed point distribution and critical exponents (that satisfy the Chayes inequality) are obtained to numerical precision by solving integro-differential equations. This reproduces many, but not all, of the qualitative features of the MBL phase transition that are suggested by previous numerical work and approximate RG studies: our RG might serve as a "zeroth-order" approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed.