Evaluation of the excitation spectra with diffusion Monte Carlo on an auxiliary bosonic ground state

Theoretical methods to evaluate the excitation spectra of an interacting fermionic system from the ground state of an auxiliary bosonic system are derived and tested in exactly soluble models. The ground state's instantaneous response to multiplication by an envelope function and the removal of an arbitrary effective potential is derived. The instantaneous imaginary time evolution of an arbitrary excitation is then obtained by sampling an observable on the ground-state distribution of walkers of an auxiliary bosonic system. We show that this approach can take advantage of and correct for approximate eigenstates obtained with mean-field calculations or truncated interactions. Relevant parts of the theory have been tested in soluble model systems and exhibit excellent agreement with exact analytical data, and the CI and the F12 approaches. In particular, for limited basis set expansions, this approach outperforms CI and F12 using the same input. Therefore, this auxiliary boson approach is expected to behave better than CI or variational Monte Carlo (VMC) for excitation spectra when the effects of Coulomb singularities are not fully captured with standard Jastrow factors. The potential use of this method to study realistic fermionic systems is discussed.