Green functions of interacting systems in the strongly localized regime

TL;DR

This paper introduces a method to compute the Green function in strongly localized one-dimensional many-body systems, revealing factorization properties and universal conductance distributions, supported by numerical validation.

Contribution

The authors develop a locator expansion-based approach for Green functions in strongly localized systems, demonstrating factorization and universality in conductance distributions.

Findings

Green function factorizes across non-interacting regions

Conductance distribution is log-normal in the strongly localized regime

Numerical results agree with exact diagonalization at high disorder

Abstract

We have developed an approach to calculate the single-particle Green function of a one-dimensional many-body system in the strongly localized limit at zero temperature. Our approach, based on the locator expansion, sums the contributions of all possible forward scattering paths in configuration space. We demonstrate for fermions that the Green function factorizes when the system can be splited into two non interacting regions. This implies that for nearest neighbors interactions the Green function factorizes at every link connecting two sites with the same occupation. As a consequence we show that the conductance distribution function for interacting systems is log-normal, in the same universality class as for non-interacting systems. We have developed a numerical procedure to calculate the ground state and the Green function, generating all possible paths in configuration space. We compare the localization length computed with our procedure with the one obtained via exact diagonalization. The latter smoothly converges to our results as the disorder increases.