Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains

TL;DR

This study investigates the finite-size scaling of the many-body localization transition in quasi-periodic spin chains, revealing a BKT transition class and less severe finite-size effects compared to random disorder models.

Contribution

It demonstrates that the MBL transition in quasi-periodic chains belongs to the BKT class and shows reduced finite-size effects, using a cost-function approach and exact diagonalization.

Findings

MBL transition in QP chains is BKT type.

Critical disorder strength drifts sub-linearly with system size.

Double-peak structure in on-site magnetization distribution deep in ergodic regime.

Abstract

We analyze the finite-size scaling of the average gap-ratio and the entanglement entropy across the many-body localization (MBL) transition in one dimensional Heisenberg spin-chain with quasi-periodic (QP) potential. By using the recently introduced cost-function approach, we compare different scenarios for the transition using exact diagonalization of systems up to 22 lattice sites. Our findings suggest that the MBL transition in the QP Heisenberg chain belongs to the class of Berezinskii-Kosterlitz-Thouless (BKT) transition, the same as in the case of uniformly disordered systems as advocated in recent studies. Moreover, we observe that the critical disorder strength shows a clear sub-linear drift with the system-size as compared to the linear drift seen in random disordered models, suggesting that the finite-size effects in the MBL transition for the QP systems are less severe than that in the random disordered scenario. Moreover, deep in the ergodic regime, we find an unexpected double-peak structure of distribution of on-site magnetizations that can be traced back to the strong correlations present in the QP potential.