Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder systems: One-Particle Properties and Boundary Effects

TL;DR

This paper investigates the effects of disorder and boundaries on the single-particle properties of gapped quasi-one-dimensional spin systems modeled by Dirac fermions with a random mass, revealing strong correlations and boundary-induced density of states enhancements.

Contribution

It provides a detailed analysis of single-particle correlations and boundary effects in disordered Dirac fermion models of spin systems, extending understanding of low-energy properties and boundary phenomena.

Findings

Green function decays as (1/x)^{3/2} at low energies

Correlations are stronger in disordered systems than in pure ones

Boundary proximity enhances local density of states logarithmically

Abstract

Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\epsilon$, the single-particle Green function decays in real space like $G(x,\epsilon) \propto (1/x)^{3/2}$. It follows that at these energies the correlations in the disordered system are strong -- even stronger than in the pure system without the gap. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as $1/\sqrt{x}$ and the density of states saturates to its bulk value on the scale $L_\epsilon \propto \ln^2 (1/\epsilon)$. This scale is different from the Thouless localization length $\lambda_\epsilon\propto\ln (1/\epsilon)$. We also discuss some implications of these results for the spin systems and their relation to the investigations based on real-space renormalization group approach.