Reduced-basis approach to many-body localization

TL;DR

This paper introduces a reduced-basis method to study many-body localization in disordered fermionic chains, enabling analysis of larger systems and providing insights into local observable stiffnesses, though with some limitations for non-local quantities.

Contribution

It develops a reduced-basis approach for MBL studies that improves system size analysis and offers a new perspective on local observable behavior.

Findings

Stiffnesses of local observables remain finite in the MBL regime.

The reduced-basis method extends the accessible system sizes.

Limitations are observed in the method's ability to analyze non-local quantities.

Abstract

Within the standard model of many-body localization, i.e., the disordered chain of spinless fermions, we investigate how the interaction affects the many-body states in the basis of noninteracting localized Anderson states. From this starting point we follow the approach that uses a reduced basis of many-body states. Together with an extrapolation to the full basis, it proves to be efficient for the evaluation of the stiffnesses of local observables, which remain finite within the non-ergodic regime and represent the hallmark of the many-body localization (MBL). The method enables a larger span of system sizes and, within the MBL regime, allows for a more careful analysis of the size scaling of calculated quantities. On the other hand, the survival stiffness as the representative of non--local quantities, reveals limitations of the reduced-basis approach.