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Quantum Critical Dynamics of the Random Transverse Field Ising Spin Chain

Dynamical correlations of the spin and the energy density are investigated in the critical region of the random transverse-field Ising chain by numerically exact calculations in large finite systems (L<=128). The spin-spin autocorrelation function is found to decay proportional to (log t)^{-2x_m} and (log t)^{-2x_m^s} in the bulk and on the surface, respectively, with x_m and x_m^s the bulk and surface magnetization exponents, respectively. On the other hand the critical energy-energy autocorrelation functions have a power law decay, which are characterized by novel critical exponents eta_e~2.2 in the bulk and eta_e^s~2.5 at the surface, respectively. The numerical results are compared with the predictions of a scaling theory.