Disordered impenetrable two-component fermions in one dimension

TL;DR

This paper analytically investigates how different types of disorder affect phase transitions in a one-dimensional two-component fermion Hubbard model with infinite repulsion, revealing distinct localization behaviors.

Contribution

It provides an explicit analytic expression for matrix elements of a random magnetic field in the model, clarifying the impact of spin-dependent disorder on many-body localization.

Findings

Spin-independent disorder leads to Anderson localization.

Spin-dependent disorder causes a many-body localization-delocalization transition.

Analytic expressions support the physical understanding of the transition.

Abstract

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion (t-0 model) in the presence of disorder. Our analytical treatment demonstrates that the type of disorder drastically changes the nature of the emerging phases. The case of spin-independent disorder can be treated as a single-particle problem with Anderson localization. On the contrary, recent numerical findings show that spin-dependent disorder, which can be realized as a random magnetic field, leads to the many-body localization-delocalization transition. We find an explicit analytic expression for the matrix elements of the random magnetic field between the eigenstates of the t-0 model with potential disorder on a finite lattice. Analysis of the matrix elements supports the existence of the many-body localization-delocalization transition in this system and provides an extended physical picture of the random magnetic field.