Bold diagrammatic Monte Carlo: A generic technique for polaron (and many-body?) problems

TL;DR

This paper introduces a versatile Monte Carlo method for sampling Feynman diagram series in many-body problems, effectively handling sign problems and divergences, with applications to polaron and Fermi gas systems.

Contribution

It presents a self-consistent diagrammatic Monte Carlo approach that uses renormalized propagators to overcome divergence and sign issues in many-body series.

Findings

Successfully applied to polaron problems in Fermi gases.

Developed a sign-problem tolerant numerical method.

Provides insights into the BCS-BEC crossover regime.

Abstract

We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single spin-down fermion resonantly interacting with the Fermi gas of spin-up particles. Though the original series based on bare propagators are sign-alternating and divergent one can still determine the answer behind them by using two strategies (separately or together): (i) using proper series re-summation techniques, and (ii) introducing renormalized propagators which are defined in terms of the simulated proper self-energy, i.e. making the entire scheme self-consistent. Our solution is important for understanding the phase diagram and properties of the BCS-BEC crossover in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem tolerant method for exact numerical solution of polaron-type models, and, possibly, of the interacting many-body Hamiltonians.