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

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 $z(δ)$, where $δ$ measures the deviation from criticality. There are some discrepancies between the values of $z(δ)$ 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 $τ^{-1/z(δ)}$, where $τ$ is imaginary time. However, the typical value decays with a stretched exponential behavior, $\exp(-cτ^{1/μ})$, where $μ$ may be related to $z(δ)$. We also obtain results for the full probability distribution of time dependent correlation functions at different points in the paramagnetic phase.