Combining branching random walks with Metropolis sampling: constraint release in auxiliary-field quantum Monte Carlo*

We present an approach to combine the branching random walks of auxiliary-field quantum Monte Carlo (AFQMC) with Markov chain Monte Carlo sampling. The formulation of branching random walks along imaginary-time is required to realize a constraint on the paths to control the sign or phase problem, according to an exact gauge condition which, in practice, is implemented approximately with a trial wave function or trial density matrix. We use the generalized Metropolis algorithm to sample a selected portion of the imaginary-time path after it has been produced by the branching random walk. This allows a constraint release to follow seamlessly from the constrained-path sampling, which can reduce the systematic error from the latter. It also provides a way to improve the computation of correlation functions and observables which do not commute with the Hamiltonian. We illustrate the method in a number of atoms/molecules, where improvements in accuracy are observed and near-exact results are obtained. 

Flatiron Institute is a division of the Simons Foundation.