Error analysis of free probability approximations to the density of states of disordered systems

TL;DR

This paper evaluates the accuracy of free probability methods in approximating the density of states in disordered systems, providing an error analysis and identifying highly accurate approximations.

Contribution

It introduces a generalized moment expansion for error quantification and compares different approximations, highlighting an eighth-moment accurate method.

Findings

An approximation accurate to the eighth moment across all noise strengths.

Error analysis distinguishes between different free probability approximations.

Contrast with perturbation and isotropic entanglement theories.

Abstract

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with the perturbation theory and isotropic entanglement theory.