An Effective Theory for Midgap States in Doped Spin Ladder and Spin-Peierls Systems: Liouville Quantum Mechanics

TL;DR

This paper demonstrates that midgap states in disordered gapped spin systems can be modeled using Liouville Quantum Mechanics, revealing power-law disorder-averaged correlations despite weak typical correlations.

Contribution

It introduces a novel application of Liouville Quantum Mechanics to describe the statistics of midgap states in doped spin ladder and spin-Peierls systems, linking strong correlations and disorder.

Findings

Disorder-averaged correlations follow a power-law decay.

Wave function correlations are typically weak but dominated by rare strong configurations.

Liouville Quantum Mechanics effectively models zero-energy midgap state statistics.

Abstract

In gapped spin ladder and spin-Peierls systems the introduction of disorder, for example by doping, leads to the appearance of low energy midgap states. The fact that these strongly correlated systems can be mapped onto one dimensional noninteracting fermions provides a rare opportunity to explore systems which have both strong interactions and disorder. In this paper we show that the statistics of the zero energy midgap wave functions in these models can be effectively described by Liouville Quantum Mechanics. This enables us to calculate the disorder averaged N-point correlation functions of these states (the explicit calculation is performed for N=2,3). We find that whilst these midgap states are typically weakly correlated, their disorder averaged correlation 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 configurations.