  We first review, following our earlier studies, the critical behavior of the
quantum Sherrington-Kirkpatrick (SK) model at finite as well as at zero
temperatures. Through the analysis of the Binder cumulant we determined the
entire phase diagram of the model and from the scaling analysis of the
numerical data we obtained the correlation length exponent. For both the
critical Binder cumulant and the correlation length exponent, we observed a
crossover from classical- to quantum-fluctuation-dominated values at a finite
temperature. We studied the behavior of the order parameter distribution of the
model in the glass phase (at finite and zero temperatures). Along with a
classical-fluctuation-dominated nonergodic region (where the replica symmetry
is broken), we also found a quantum-fluctuation-dominated low-temperature
ergodic region in the spin glass phase. In this quantum-fluctuation-dominated
region, the order parameter distribution has a narrow peak around its most
probable value, eventually becoming a delta function in the
infinite-system-size limit (indicating replica symmetry restoration or
ergodicity in the system). We also found that the annealing time (to reach a
very low energy level of the classical SK model) becomes practically
system-size-independent when the annealing paths pass through this ergodic
region. In contrast, when such paths pass through the nonergodic region, the
convergence time grows rapidly with the system size. We present a new study of
the autocorrelation of the spins in both ergodic and nonergodic regions. We
found a significant increase in the relaxation time (and also a change in the
relaxation behavior) in the classical-fluctuation-dominated (nonergodic) region
compared with that in the quantum-fluctuation-dominated (ergodic) region of the
spin glass phase.
