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

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 Fréchet form. Relation between the Dyson-Schmidt technique and the strong disorder renormalization group method is also discussed.

7 pages, accepted for publication in Phys. Rev. B