Polaron Problem by Diagrammatic Quantum Monte Carlo

Abstract

We present a precise solution of the polaron problem by a novel Monte Carlo method. Basing on conventional diagrammatic expansion for the Green function of the polaron, $G({\bf k}, τ)$, we construct a process of generating continuous random variables ${\bf k}$ and $τ$, with the distribution function exactly coinciding with $G({\bf k}, τ)$. The polaron spectrum is extracted from the asymptotic behavior of the Green function. We compare our results for the polaron energy with the variational treatment of Feynman, and for the first time present precise dispersion curve which features an ending point at finite momentum.