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

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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, (-cτ¹/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.