Exact Numerical Calculation of the Density of States of the Fluctuating Gap Model

TL;DR

This paper introduces a highly accurate numerical method for calculating the density of states in the fluctuating gap model, revealing detailed behavior of the pseudogap regime in disordered chains.

Contribution

The authors develop a novel numerical algorithm based on solving a Riccati equation for precise density of states calculations in the fluctuating gap model.

Findings

Density of states rho(omega) can be computed with high accuracy.

Pseudogap behavior is overshadowed by a Dyson singularity below a specific energy.

Explicit calculation of the crossover energy omega* as a function of disorder correlation length xi.

Abstract

We develop a powerful numerical algorithm for calculating the density of states rho(omega) of the fluctuating gap model, which describes the low-energy physics of disordered Peierls and spin-Peierls chains. We obtain rho(omega) with unprecedented accuracy from the solution of a simple initial value problem for a single Riccati equation. Generating Gaussian disorder with large correlation length xi by means of a simple Markov process, we present a quantitative study of the behavior of rho (omega) in the pseudogap regime. In particular, we show that in the commensurate case and in the absence of forward scattering the pseudogap is overshadowed by a Dyson singularity below a certain energy scale omega^{ast}, which we explicitly calculate as a function of xi.