Localization and delocalization of fermions in a background of correlated spins

TL;DR

This paper investigates how fermions localize or delocalize in a fluctuating spin background, revealing potential localization in 2D and a mobility edge in 3D, with implications for strongly correlated electron systems.

Contribution

It introduces a lattice fermion model coupled to classical spin backgrounds via a gauge-invariant hopping term, analyzing localization phenomena in different dimensions.

Findings

In 2D, all fermion states tend to be localized.

In 3D, a mobility edge exists separating localized and delocalized states.

Critical temperature for localization-delocalization transition depends on fermion concentration.

Abstract

We study the (de)localization phenomena of one-component lattice fermions in spin backgrounds. The O(3) classical spin variables on sites fluctuate thermally through the ordinary nearest-neighbor coupling. Their complex two-component (CP$^1$-Schwinger boson) representation forms a composite U(1) gauge field on bond, which acts on fermions as a fluctuating hopping amplitude in a gauge invariant manner. For the case of antiferromagnetic (AF) spin coupling, the model has close relationship with the $t$-$J$ model of strongly-correlated electron systems. We measure the unfolded level spacing distribution of fermion energy eigenvalues and the participation ratio of energy eigenstates. The results for AF spin couplings suggest a possibility that, in two dimensions, all the energy eigenstates are localized. In three dimensions, we find that there exists a mobility edge, and estimate the critical temperature $T_{\ss LD}(\delta)$ of the localization-delocalization transition at the fermion concentration $\delta$.