UBC Theses and Dissertations
Polaron physics beyond the Holstein model Marchand, Dominic
Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.
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