Ground-state dispersion and density of states from path-integral Monte Carlo: Application to the lattice polaron

A formula is derived that relates the ground-state dispersion of a many-bod y system with the end-to-end distribution of paths with open boundary condi tions in imaginary time. The formula does not involve the energy estimator. It allows direct measurement of the ground-state dispersion by quantum Mon te Carlo methods without analytical continuation or auxiliary fitting. The formula is applied to the lattice polaron problem. The exact polaron spectr um and density of states are calculated for several models in one, two, and three dimensions. In the adiabatic regime of the Holstein model, the polar on density of states deviates spectacularly from the free-particle shape. [ S0163-1829(99)05529-0].