Electronic structure via the auxiliary-field Monte Carlo algorithm

Abstract

Auxiliary-field Monte Carlo (AFMC) is an exact approach for calculating the ground state of a system of fermions (or bosons) interacting by pair-potentials. The method uses the Hubbard–Stratonovich transformation to replace the exact imaginary-time propagator by an average over an ensemble of propagators for independent particles in the presence of a varying external field, so that the calculation of the exact energy is reduced to multiple independent calculations, each of which costs essentially the same as one Hartree–Fock iteration. Here we consider the application of AFMC to calculate molecular structure, and present preliminary simulations on He and Be. We develop two simple methods to partially alleviate a ‘‘sign-problem’’ in AFMC through restriction of the length of the imaginary-time propagation, by either a simultaneous propagation of several initial states followed by subspace-diagonalization or by incorporation of information from all propagated time steps. The first method is tested and found to yield significant improvement in accuracy. For the present simulations, the single-particle orbitals are expanded in a given set of primitive orbitals. The resulting spectral-AFMC method yields, for sufficiently converged ensembles, the full-CI energy associated with a given basis. The developments reported here, and in particular the demonstration of subspace-diagonalization, have however general validity independent of whether a basis set or a grid representation is used for the single-particle orbitals (in the first case a full-CI result is obtained in the given basis, while a converged grid representation would yield the exact result).