ELECTRONIC-STRUCTURE VIA THE AUXILIARY-FIELD MONTE-CARLO ALGORITHM

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). © 1995 American Institute of Physics.