Diagrammatic Monte Carlo method as applied to the polaron problems
Cross-Correlated Materials Research Group (CMRG), ASI, RIKEN, Wako, Saitama , Japan
Numerical methods whereby exact solutions to the problem of a few particles interacting with one another and with
several bosonic excitation branches are presented. The diagrammatic Monte Carlo method allows the exact calculation
of the Matsubara Green function, and the stochastic optimization technique provides an approximation-free analytic continuation. In this review, results unobtainable by conventional methods are discussed, including the properties of excited
states in the self-trapping phenomenon, the optical spectra of polarons in all coupling regimes, the validity range analysis of
the Frenkel and Wannier approximations relevant to the exciton, and the peculiarities of photoemission spectra of a lattice-
coupled hole in a Mott insulator.