Many-body localization near the critical point

TL;DR

This paper analyzes the many-body localization transition in one-dimensional quantum systems, revealing a new universality class with unique critical behavior distinct from the Kosterlitz-Thouless transition.

Contribution

The study provides an analytical determination of the critical behavior of the MBL transition using a strong-randomness RG approach, identifying a new universality class.

Findings

Critical behavior is analytically determined within RG framework.

The MBL transition exhibits a new universality class, different from KT.

Correlation length divergence has an infinite critical exponent , weaker than KT.

Abstract

We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough $\textit{qualitative}$ level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus we show that this MBL transition is in a new universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $\nu \rightarrow \infty$, but the divergence is weaker than for the KT transition.