Polaron Problem by Diagrammatic Quantum Monte Carlo

We present a numerical solution of the polaron problem by a novel Monte Carlo method. Starting from a conventional diagrammatic expansion for the polaron Green function $G(\mathbf{k},\tau )$, we construct a process which generates continuous random variables $\mathbf{k}$ and $\tau$, with a distribution function coinciding exactly with $G(\mathbf{k},\tau )$. 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 present an accurate dispersion curve which features an end point at finite momentum.