Zero-modes and thermodynamics of disordered spin-1/2 ladders

The influence of non-magnetic doping on the thermodynamic properties of two -leg S = 1/2 spin ladders is studied in this paper. It is shown that, for a weak interchain coupling, the problem can be mapped onto a model of random mass Dirac (Majorana) fermions. We investigate in detail the structure of the fermionic states localized at an individual mass kink (zero-modes) in t he framework of a generalized Dirac model. The low-temperature thermodynami c properties are dominated by these zero-modes. We use the single-fermion d ensity of states, known to exhibit the Dyson singularity in the zero-energy limit, to construct the thermodynamics of the spin ladder, In particular, we find that the magnetic susceptibility chi diverges at T --> 0 as 1/Tln(2 )(1/T), and the specific heat behaves as C proportional to 1/ln(3)(1/T). Th e predictions on magnetic susceptibility are consistent with the most recen t results of quantum Monte Carlo simulations on doped ladders with randomly distributed impurities. We also calculate the average staggered magnetic s usceptibility induced in the system by such defects. (C) 1999 Elsevier Scie nce B.V.