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.

PACS: 02.70.Uu, 71.35.−y, 71.38.−k, 74.72.−h (all) DOI: 10.1070/PU2005v048n09ABEH002632 URL: https://ufn.ru/en/articles/2005/9/b/ 000234905700002 2005PhyU...48..887M Citation: Mishchenko A S "Diagrammatic Monte Carlo method as applied to the polaron problems" Phys. Usp. 48 887–902 (2005) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Мищенко А С «Диаграммный метод Монте-Карло в применении к проблемам поляронов» УФН 175 925–942 (2005); DOI: 10.3367/UFNr.0175.200509b.0925