Fermionic many-body localization for random and quasiperiodic systems in the presence of short- and long-range interactions

TL;DR

This paper investigates how the range of interactions affects many-body localization in one-dimensional fermionic systems with disorder, revealing distinct behaviors for short- and long-range interactions through numerical analysis.

Contribution

It provides the first detailed phase diagrams of MBL in fermionic systems considering both short- and long-range interactions, highlighting the absence of symmetry in the long-range case.

Findings

Long-range interactions lead to persistent MBL regardless of disorder strength.

Short-range interactions show symmetry between weak and strong interaction regimes.

Scaling exponents suggest different MBL regimes influenced by interaction range.

Abstract

We study many-body localization (MBL) for interacting one-dimensional lattice fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing on the role of interaction range. We obtain the MBL quantum phase diagrams by calculating the experimentally relevant inverse participation ratio (IPR) at half-filling using exact diagonalization methods and extrapolating to the infinite system size. For short-range interactions, our results produce in the phase diagram a qualitative symmetry between weak and strong interaction limits. For long-range interactions, no such symmetry exists as the strongly interacting system is always many-body localized, independent of the effective disorder strength, and the system is analogous to a pinned Wigner crystal. We obtain various scaling exponents for the IPR, suggesting conditions for different MBL regimes arising from interaction effects.