# Two universality classes for the many-body localization transition

## TL;DR

This paper compares the many-body localization transition in spin chains with quasiperiodic and random fields, revealing two distinct universality classes and highlighting differences in finite-size effects and phase stability.

## Contribution

It identifies two separate universality classes for the MBL transition and emphasizes the importance of quasiperiodic models in understanding the transition.

## Key findings

- Two universality classes identified: quasiperiodic and random.
- Finite-size effects differ significantly between models.
- MBL phase is more stable in quasiperiodic systems.

## Abstract

We provide a systematic comparison of the many-body localization transition in spin chains with nonrandom quasiperiodic vs. random fields. We find evidence that these belong to two separate universality classes: one dominated by "intrinsic" intra-sample randomness, and the second dominated by external inter-sample quenched randomness. We show that the effects of inter-sample variations are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the quenched-disorder dominated universality class. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects. Altogether, our results motivate the need for a greater focus on quasiperiodic models in theoretical studies of the MBL transition.