Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome

TL;DR

This paper presents a novel Monte Carlo method called bold diagrammatic Monte Carlo that leverages a moderate sign problem to achieve broader convergence in solving integral equations and many-body problems.

Contribution

It introduces a new Monte Carlo scheme that uses bold-line diagrammatic series, expanding convergence and turning the sign problem into an advantage.

Findings

Successfully solves a one-particle s-scattering problem

Calculates T-matrix for a fermipolaron system

Demonstrates broader convergence compared to traditional methods

Abstract

We introduce a Monte Carlo scheme for sampling bold-line diagrammatic series specifying an unknown function in terms of itself. The range of convergence of this bold(-line) diagrammatic Monte Carlo (BMC) is significantly broader than that of a simple iterative scheme for solving integral equations. With BMC technique, a moderate "sign problem" turns out to be an advantage in terms of the convergence of the process. For an illustrative example, we solve one-particle s-scattering problem. As an important application, we obtain T-matrix for a fermipolaron (one spin-down particle interacting with the spin-up fermionic sea).