A self-consistent Hartree-Fock approach to Many-Body Localization

TL;DR

This paper introduces a self-consistent Hartree-Fock method to study many-body localization in interacting fermions, capturing key phenomenology and effects of disorder and quasiperiodic potentials.

Contribution

The work develops a simplified Hartree-Fock framework that incorporates spatial fluctuations and rare-region effects to analyze MBL dynamics.

Findings

Weak disorder leads to rapid density profile equilibration.

Strong disorder results in frozen density profiles and coherent self-energy oscillations.

Rare-region effects cause subdiffusive relaxation in random systems, absent in quasiperiodic potentials.

Abstract

In this work, we develop a self-consistent Hartree-Fock approach to theoretically study the far-from-equilibrium quantum dynamics of interacting fermions, and apply this approach to explore the onset of many-body localization (MBL) in these systems. We investigate the dynamics of a state with a nonequilibrium density profile; we find that at weak disorder the density profile equilibrates rapidly, whereas for strong disorder it remains frozen on the accessible timescales. We analyze this behavior in terms of the Hartree-Fock self-energy. At weak disorder the self-energy fluctuates strongly and can be interpreted as a self-consistent noise process. By contrast, at strong disorder the self-energy evolves with a few coherent oscillations which cannot delocalize the system. Accordingly, the non-equilibrium site-resolved spectral function shows a broad spectrum at weak disorder and sharp spikes at strong disorder. Our Hartree-Fock theory incorporates spatial fluctuations and rare-region effects. As a consequence, we find subdiffusive relaxation in random systems; but, when the system is subjected to weak quasi-periodic potentials, the subdiffusive response ceases to exist, as rare region effects are absent in this case. This self-consistent Hartree-Fock approach can be regarded as a relatively simple theory that captures much of the MBL phenomenology.