Universal properties of many-body localization transitions in quasiperiodic systems

TL;DR

This paper investigates the nature of many-body localization (MBL) transitions in one-dimensional quasiperiodic systems using real-space renormalization group methods, revealing a critical exponent that suggests stability against weak disorder and potential universality.

Contribution

The study provides the first detailed analysis of MBL transitions in 1D quasiperiodic systems, showing they share a critical exponent with random systems and are stable against weak disorder.

Findings

MBL transition in 1D QP systems has a critical exponent ~2.4.

This exponent respects bounds indicating stability against weak disorder.

MBL transitions in QP systems may belong to the same universality class as in random systems.

Abstract

Precise nature of MBL transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here we investigate MBL transitions in one-dimensional ($d\!=\!1$) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent $\nu\!\approx\!2.4$, which respects the Harris-Luck bound ($\nu\!>\!1/d$) for QP systems. Note that $\nu\!\approx\! 2.4$ for QP systems also satisfies the Harris-CCFS bound ($\nu\!>\!2/d$) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure $\nu$ of QP-induced MBL transitions.