Griffiths-McCoy singularities in random quantum spin chains: Exact results

TL;DR

This paper provides exact results on Griffiths-McCoy singularities in random quantum spin chains, analyzing their low-energy excitations and statistical properties using the Dyson-Schmidt method.

Contribution

It offers a precise calculation of the density of states and links between Dyson-Schmidt and strong disorder renormalization group techniques.

Findings

Low-energy excitations follow Fréchet distribution.

Density of states calculated exactly for off-critical chains.

Statistics of excitations follow extreme value theory.

Abstract

We consider random quantum (tight-binding, XX and Ising) spin chains in the off-critical region and study their Griffiths-McCoy singularities. These are obtained from the density of states of the low-energy excitations, which is calculated exactly by the Dyson-Schmidt method. In large finite systems the low-energy excitations are shown to follow the statistics of extremes and their distribution is given by the Fr\'echet form. Relation between the Dyson-Schmidt technique and the strong disorder renormalization group method is also discussed.