Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations

We introduce a new stochastic method for calculating ground-state properties of quantum systems. Segments of a Langevin random walk guided by a trial wave function are subject to a Metropolis rejection test performed on the time integral of the local energy. The algorithm—which is as simple as variational Monte Carlo—for bosons provides exact expectation values of local observables, as well as their static and dynamic (in imaginary time) response functions, without mixed-estimate nor population-control biases. Our method is demonstrated with a few case applications to ${}^4\mathrm{He}$.