Abstract
Numerical methods whereby exact solutions to theproblem of a few particles interacting with one another and withseveral bosonic excitation branches are presented. The diagrammatic Monte Carlo method allows the exact calculationof the Matsubara Green function, and the stochastic optimization technique provides an approximation-free analytic continuation. In this review, results unobtainable by conventionalmethods are discussed, including the properties of excitedstates in the self-trapping phenomenon, the optical spectra ofpolarons in all coupling regimes, the validity range analysis ofthe Frenkel and Wannier approximations relevant to the exciton, and the peculiarities of photoemission spectra of a lattice-coupled hole in a Mott insulator.
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