RANDOM-MASS DIRAC FERMIONS IN DOPED SPIN-PEIERLS AND SPIN-LADDER SYSTEMS - ONE-PARTICLE PROPERTIES AND BOUNDARY EFFECTS

Quasi-one-dimensional spin-Peierls and spin-ladder systems are charact erized 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 Dyso n 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 Berezinski i's diagram technique. We find that, at low energy epsilon, the single -particle Green function decays in real space like G(x,epsilon) propor tional to (1/x)(3/2). It follows that at these energies the correlatio ns in the disordered system are strong - even stronger than in the pur e system without the gap. At distances x similar to L-epsilon proporti onal to ln(2)(1/epsilon), the Green function crosses over to a standar d exponential decay. The scale L-epsilon is different from the Thoules s localization length lambda(epsilon) proportional to ln(1/epsilon). A dditionally, we study the effects of boundaries on the local density o f states. We find that the latter is logarithmically (in the energy) e nhanced close to the boundary. This enhancement decays into the bulk a s 1/root x saturating at x similar to L-epsilon. We also discuss some implications of these results for the spin systems and their relation to the investigations based on the real-space renormalization group ap proach.