Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series

TL;DR

This paper introduces a Monte Carlo method to accurately solve divergent, sign-alternating diagrammatic series in polaron models, advancing understanding of strongly imbalanced fermionic systems and the BCS-BEC crossover.

Contribution

It develops a generic, sign-problem tolerant Monte Carlo approach for exact numerical solutions of polaron models, applicable to divergent series.

Findings

First application of Monte Carlo to divergent sign-alternating series

Provides insights into the phase diagram of imbalanced fermionic systems

Enhances understanding of the BCS-BEC crossover in strongly interacting regimes

Abstract

Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical solution of polaron-type models. On the other hand, our solution is important for understanding the phase diagram and properties of the BCS-BEC crossover in the strongly imbalanced regime. This is the first, and possibly characteristic, example of how the Monte Carlo approach can be applied to a divergent sign-alternating diagrammatic series.