Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain

TL;DR

This paper numerically investigates the finite temperature and dynamical properties of the random transverse-field Ising chain, revealing Griffiths-McCoy singularities and contrasting average and typical correlation decay behaviors.

Contribution

It extends previous work to include finite temperatures and dynamical properties, providing new insights into correlation functions and Griffiths phases in the disordered chain.

Findings

Average correlation decays as a power law with imaginary time.

Typical correlation exhibits stretched exponential decay.

Results support the presence of Griffiths-McCoy singularities.

Abstract

We study numerically the paramagnetic phase of the spin-1/2 random transverse-field Ising chain, using a mapping to non-interacting fermions. We extend our earlier work, Phys. Rev. 53, 8486 (1996), to finite temperatures and to dynamical properties. Our results are consistent with the idea that there are ``Griffiths-McCoy'' singularities in the paramagnetic phase described by a continuously varying exponent $z(\delta)$, where $\delta$ measures the deviation from criticality. There are some discrepancies between the values of $z(\delta)$ obtained from different quantities, but this may be due to corrections to scaling. The average on-site time dependent correlation function decays with a power law in the paramagnetic phase, namely $\tau^{-1/z(\delta)}$, where $\tau$ is imaginary time. However, the typical value decays with a stretched exponential behavior, $\exp(-c\tau^{1/\mu})$, where $\mu$ may be related to $z(\delta)$. We also obtain results for the full probability distribution of time dependent correlation functions at different points in the paramagnetic phase.