Quasi-adiabatic Quantum Monte Carlo algorithm for non-equilibrium quantum phase transitions

We investigate a new quantum Monte Carlo algorithm for studying static and dynamic properties of quantum phase transitions. The method, called the quasi-adiabatic quantum Monte Carlo algorithm, is based on evolution with a changing Hamiltonian to derive information pertinent to a quantum quench according to an arbitrary protocol. We demonstrate the method with results for 1D and 2D transverse-field Ising models, showing finite-size and finite-velocity scaling according to a generalization of the Kibble-Zurek mechanism. We explore ways to extract critical points and critical exponents to high precision.