Polaron Problem by Diagrammatic Quantum Monte Carlo

TL;DR

This paper introduces a novel Monte Carlo method to solve the polaron problem precisely by generating continuous random variables based on the Green function, enabling accurate energy and dispersion calculations.

Contribution

It presents a new Monte Carlo approach for the polaron problem that improves accuracy and provides detailed dispersion curves with an ending point at finite momentum.

Findings

Accurate polaron energy calculations matching variational results

First precise dispersion curve with an ending point at finite momentum

Method enables direct extraction of spectral properties from Green functions

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, $G({\bf k}, \tau)$, we construct a process of generating continuous random variables ${\bf k}$ and $\tau$, with the distribution function exactly coinciding with $G({\bf k}, \tau)$. 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 for the first time present precise dispersion curve which features an ending point at finite momentum.