Disordered Boson Systems: A Perturbative Study

TL;DR

This paper investigates the effects of weak disorder on disordered boson systems by mapping them to quantum spin models and applying a 1/S expansion, revealing how disorder impacts phonon properties.

Contribution

It introduces a perturbative 1/S expansion approach to analyze weak disorder effects in disordered boson systems mapped onto quantum spin models.

Findings

Disorder reduces the speed of sound in the system.

Disorder affects the lifetime of Bloch phonons.

The study discusses potential extensions to strong disorder regimes.

Abstract

A hard-core disordered boson system is mapped onto a quantum spin 1/2 XY-model with transverse random fields. It is then generalized to a system of spins with an arbitrary magnitude S and studied through a 1/S expansion. The first order 1/S expansion corresponds to a spin-wave theory. The effect of weak disorder is studied perturbatively within such a first order 1/S scheme. We compute the reduction of the speed of sound and the life time of the Bloch phonons in the regime of weak disorder. Generalizations of the present study to the strong disordered regime are discussed.