title: Diagrammatic Monte Carlo method for many-polaron problems.
abstract: We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at a finite electron density nonperturbatively, i.e., by including vertex corrections to high orders. Using the Holstein model on a square lattice as a prototypical example, we demonstrate that our method is capable of providing accurate results in the thermodynamic limit in all regimes from a renormalized Fermi liquid to a single polaron, across the nonadiabatic region where Fermi and Debye energies are of the same order of magnitude. By accounting for vertex corrections, the accuracy of the theoretical description is increased by orders of magnitude relative to the lowest-order self-consistent Born approximation employed in most studies. We also find that for the electron-phonon coupling typical for real materials, the quasiparticle effective mass increases and the quasiparticle residue decreases with increasing the electron density at constant electron-phonon coupling strength.
authors.affiliation: RIKEN Center for Emergent Matter Science (CEMS), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan and Russian Research Center Kurchatov Institute, 123182 Moscow, Russia.
authors.forename: Andrey S
authors.initials: AS
authors.lastname: Mishchenko
authors.affiliation: RIKEN Center for Emergent Matter Science (CEMS), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan and Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan.
authors.forename: Naoto
authors.initials: N
authors.lastname: Nagaosa
authors.affiliation: Russian Research Center Kurchatov Institute, 123182 Moscow, Russia and Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
authors.forename: Nikolay
authors.initials: N
authors.lastname: Prokof'ev