Symmetry constraints and variational principles in diffusion quantum MonteCarlo calculations of excited-state energies

Fixed-node diffusion Monte Carlo (DMC) is a stochastic algorithm for findin g the lowest energy many-fermion wave function with the same nodal surface as a chosen trial function. It has proved itself among the most accurate me thods available for calculating many-electron,ground states, and is one of the few approaches that can be applied to systems large enough to act as re alistic models of solids. In attempts to use fixed-node DMC for excited-sta te calculations, it has often been assumed that the DMC energy must be grea ter than or equal to the energy of the lowest exact eigenfunction with the same symmetry as the trial function. We show that this assumption is not ju stified unless the trial function transforms according to a one-dimensional irreducible representation of the symmetry group of the Hamiltonian. If th e trial function transforms according to a multidimensional irreducible rep resentation, corresponding to a degenerate energy level, the DMC energy may lie below the energy of the lowest eigenstate of that symmetry. Weaker var iational bounds may then be obtained by choosing trial functions transformi ng according to one-dimensional irreducible representations of subgroups of the full symmetry group. [S0163-1829(99)09331-5].