Dynamics of strongly interacting systems: From Fock-space fragmentation to Many-Body Localization

TL;DR

This paper investigates the dynamics of a strongly interacting disordered fermionic system, revealing Hilbert space fragmentation, localization phenomena, and a transition to many-body localization with complex dynamical behavior.

Contribution

It provides an exact mapping for certain blocks to Anderson models and characterizes the MBL transition in the system's Hilbert space structure.

Findings

Localized eigenstates in single-mover blocks for any disorder

Existence of an MBL transition at finite disorder

Evidence of diffusive and sub-diffusive dynamics near the transition

Abstract

We study the $t{-}V$ disordered spinless fermionic chain in the strong coupling regime, $t/V\rightarrow 0$. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: Blocks with only one mover and the ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show an MBL transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe sub-diffusive dynamics at finite time scales and find indications that this might be only a transient behavior before crossing over to diffusion.