Quasi-adiabatic quantum Monte Carlo algorithm for quantum evolution in imaginary time

Understand

We propose a quantum Monte Carlo (QMC) algorithm for non-equilibrium dynamics in a system with a parameter varying as a function of 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 non-adiabatic 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.