Analytical Results for Random Band Matrices with Preferential Basis

TL;DR

This paper analytically investigates the spectral and localization properties of a class of random band matrices with preferential basis, extending known results and confirming them with numerical data.

Contribution

It introduces an analytical approach to study random band matrices with preferential basis, expanding the understanding beyond ordinary band matrices.

Findings

Analytical expressions for local density of states and localization length.

Distribution function of eigenvector components derived.

Results agree with recent numerical simulations.

Abstract

Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a random band matrix with a strongly fluctuating diagonal matrix. In this way we extend previously known results for ordinary band matrices to the class of random band matrices with preferential basis. Our analytical results are in good agreement with (but more general than) recent numerical findings by Jacquod and Shepelyansky.