We propose a quantum Monte Carlo (QMC) algorithm for nonequilibrium dynamics in a system with a parameter varying as a function of imaginary time. The method is based on successive applications of an evolving Hamiltonian to an initial state and delivers results for a whole range of the tuning parameter in a single run, allowing for access to both static and dynamic properties of the system. This approach reduces to the standard Schr\"odinger dynamics in imaginary time for quasi-adiabatic evolutions, i.e., including the leading nonadiabatic correction to the adiabatic limit. We here demonstrate this quasi-adiabatic QMC (QAQMC) method for linear ramps of the transverse-field Ising model across its quantum-critical point in one and two dimensions. The critical behavior can be described by generalized dynamic scaling. For the two-dimensional square-lattice system, we use the method to obtain a high-precision estimate of the quantum-critical point
(h/J)c=3.04458(7), where
h is the transverse magnetic field and
J is the nearest-neighbor Ising coupling. The QAQMC method can also be used to extract the Berry curvature and the metric tensor.
We study with exact diagonalization techniques the Heisenberg model for a system of SU(2) spins with
S=1/2 and random infinite-range exchange interactions. We calculate the critical temperature
Tg for the spin-glass to paramagnetic transition. We obtain ${T}_{g}\ensuremath{\approx}0.13,$ in good agreement with previous quantum Monte Carlo and analytical estimates. We provide a detailed picture for the different kind of excitations which intervene in the dynamical response ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega},T)$ at
T=0 and analyze their evolution as T increases. We also calculate the specific heat
Cv(T). We find that it displays a smooth maximum at ${T}_{M}\ensuremath{\approx}0.25,$ in good qualitative agreement with experiments. We argue that the fact that
TM>Tg is due to a quantum disorder effect.
We study the zero-temperature behaviour of the infinite-ranged Ising spin glass in a transverse field. Using spin summation and Monte Carlo methods we characterize the zero-temperature quantum transition. Our results are well compatible with a value for the correlation length exponent, z=4 for the dynamical exponent and an algebraic decay for the imaginary-time correlation function. The zero-temperature Monte Carlo relaxation of the energy in the presence of the transverse field shows that the system monotonically reaches the ground-state energy due to quantum fluctuations and displays glassy effects due to the strong anisotropy in the effective Hamiltonian.