Auxiliary boson diffusion Monte Carlo approach for excitations

A theoretical method to evaluate the excitation spectra of an interacting system from the ground state of an auxiliary system is presented and tested in a model system. The imaginary time evolution of an arbitrary state can be obtained by sampling the ground state distribution of walkers, and the gradients of the distribution of walkers of an auxiliary bosonic system. The wave-function of each excitation is expanded into a product of bosonic and fermionic wavefunctions. The bosonic function is treated statistically in DMC while the fermionic part is expanded in a basis and evaluated numerically. A fermion-boson coupling term appears that can be sampled on the bosonic ground state. The bosonic factor is expected to reduce the size of the basis required by the fermionic component: we show it incorporates in DMC the correlations missed by standard Jastrow factors. The implementation of this method in current DMC codes will be facilitated by reuse of procedures already developed and tested for the calculation of ground state properties with DMC or excitations with variational Monte Carlo(VMC). The perspectives and potential problems of this method when applied to realistic fermionic systems are discussed.