Complex random matrix models with possible applications to spin- impurity scattering in quantum Hall fluids

TL;DR

This paper analyzes complex random matrix models to understand spin-dependent impurity scattering in quantum Hall fluids, revealing spectral singularities and extending to lattice models of arbitrary dimensions.

Contribution

It introduces a detailed analysis of Green's functions in complex random matrices applied to quantum Hall impurity scattering, including generalized lattice models.

Findings

Density of states exhibits a singularity at the band center.

Green's functions computed to sub-leading orders in large N limit.

Model applicable to spin-dependent impurity scattering in quantum Hall systems.

Abstract

We study the one-point and two-point Green's functions in a complex random matrix model to sub-leading orders in the large N limit. We take this complex matrix models as a model for the two-state scattering problem, as applied to spin dependent scattering of impurities in quantum Hall fluids. The density of state shows a singularity at the band center due to reflection symmetry. We also compute the one-point Green's function for a generalized situation by putting random matrices on a lattice of arbitrary dimensions.