Transport properties across the many-body localization transition in quasiperiodic and random systems

TL;DR

This paper investigates transport behavior across the many-body localization transition in one-dimensional quasiperiodic and random systems, revealing differences in robustness and scaling properties through exact diagonalization analysis.

Contribution

It provides a comparative analysis of transport properties in quasiperiodic and random models, highlighting the distinct nature of their MBL transitions and the limitations of activated dynamical scaling.

Findings

Quasiperiodic models show more robust diffusive and MBL regimes than random models.

Activated dynamical scaling applies well to random but not quasiperiodic systems.

Critical eigenstates in quasiperiodic systems lead to a subdiffusive crossover near the MBL transition.

Abstract

We theoretically study transport properties in one-dimensional interacting quasiperiodic systems at infinite temperature. We compare and contrast the dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic and random models. Using exact diagonalization we compute the optical conductivity $\sigma(\omega)$ and the return probability $R(\tau)$ and study their average low-frequency and long-time power-law behavior, respectively. We show that the low-energy transport dynamics is markedly distinct in both the thermal and MBL phases in quasiperiodic and random models and find that the diffusive and MBL regimes of the quasiperiodic model are more robust than those in the random system. Using the distribution of the DC conductivity, we quantify the contribution of sample-to-sample and state-to-state fluctuations of $\sigma(\omega)$ across the MBL transition. We find that the activated dynamical scaling ansatz works poorly in the quasiperiodic model but holds in the random model with an estimated activation exponent $\psi\approx 0.9$. We argue that near the MBL transition in quasiperiodic systems, critical eigenstates give rise to a subdiffusive crossover regime on finite-size systems.