Phase phonon spectrum and melting in a quantum rotor model with diagonal disorder

TL;DR

This paper investigates the effects of on-site disorder on the phase phonon spectrum and quantum melting in a disordered quantum rotor model, relevant for superconducting grains and superfluid helium, using CPA and Lindemann criterion.

Contribution

It introduces a harmonic approximation approach with CPA to analyze disorder effects and estimates quantum melting parameters in the model.

Findings

Disorder broadens the density of states and reduces excitation lifetimes.

The study estimates critical parameters for quantum melting at zero temperature.

Provides insights into phase stability in disordered quantum rotor systems.

Abstract

We study the zero-temperature ($T = 0$) quantum rotor model with on-site disorder in the charging energy. Such a model may serve as an idealized Hamiltonian for an array of Josephson-coupled small superconducting grains, or superfluid $^4$He in a disordered environment. In the approximation of small-amplitude phase fluctuations, the Hamiltonian maps onto a system of coupled harmonic oscillators with on-site disorder. We study the effects of disorder in this harmonic regime, using the coherent potential approximation (CPA), obtaining the density of states and the lifetimes of the spin-wave-like excitations for several choices of the parameters which characterize the disorder. Finally, we estimate the parameters characterizing the $T = 0$ quantum melting of the phase order, using a suitable Lindemann criterion.