Quantum dynamics of an Ising spin-chain in a random transverse field

TL;DR

This paper investigates the quantum dynamics of an Ising spin-chain in a random transverse field, revealing how disorder affects excitation spectra and dispersion, with implications for neutron scattering experiments.

Contribution

It introduces numerical analysis of the dynamic structure factor in a disordered Ising chain using Jordan-Wigner transformation, exploring different magnetic field distributions.

Findings

Dispersing branch observed with rectangular distribution

Disorder broadens dispersion peaks and closes the excitation gap

Non-dispersing branch at zero energy with binary distribution

Abstract

We consider an Ising spin-chain in a random transverse magnetic field and compute the zero temperature wave vector and frequency dependent dynamic structure factor numerically by using Jordan-Wigner transformation. Two types of distributions of magnetic fields are introduced. For a rectangular distribution, a dispersing branch is observed, and disorder tends to broaden the dispersion peak and close the excitation gap. For a binary distribution, a non-dispersing branch at almost zero energy is recovered. We discuss the relationship of our work to the neutron scattering measurement in $\mathrm{LiHoF_4}$.