EFFECTIVE THEORY FOR MIDGAP STATES IN DOPED SPIN-LADDER AND SPIN-PEIERLS SYSTEMS - LIOUVILLE QUANTUM-MECHANICS

In gapped spin-ladder and spin-Peierls systems the introduction of dis order, for example by doping, leads to the appearance of low-energy mi dgap states. The fact that these strongly correlated systems can be ma pped onto one-dimensional noninteracting fermions provides a rare oppo rtunity to explore systems that have both strong interactions and diso rder. In this paper we will show that the statistics of the zero energ y midgap wave functions psi(o)(x) in these models can be effectively d escribed by Liouville quantum mechanics. This enables us to calculate averages over disorder of the products psi(o)(2)(x(1))psi(o)(2)(x(2)). ..psi(o)(2)(X-N) (the explicit calculation is performed for N= 2,3). W e find that while these midgap states are typically weakly correlated, their disorder averaged correlations are power law. This discrepancy arises because the correlations are not self-averaging and averages of the wave functions are dominated by anomalously strongly correlated c onfigurations; a fact that is not always appreciated in the literature .