Diagrammatic Monte Carlo study of the Holstein polaron

The aim of the thesis is to apply the Diagrammatic Monte Carlo numerical method [N. V. Prokof’ev and B. V. Svistunov, Phys. Rev. Lett. 81, 2514, 1998] to the Holstein model of the lattice polaron. As part of this work, the method was implemented in a computer program, and its results were collected and analyzed. The study focuses on ground state properties of the Holstein polaron, such as energy, effective mass and average number of phonons. Observables are computed via an improved approach using estimators developed by Mishchenko [A. Mishchenko et al., Phys. Rev. B, vol. 62, 09, 2009]. The dependency of polaron properties on coupling and momentum is investigated for different dimensionalities (1D, 2D and 3D). Results are compared to analytical expressions obtained in the weak-coupling and strong-coupling limits and to other approaches found in literature.