Quantum Critical Dynamics of the Random Transverse Field Ising Spin Chain

Abstract

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.