Flat histogram diagrammatic Monte Carlo method

TL;DR

This paper introduces the Flat Histogram Diagrammatic Monte Carlo method, enhancing the sampling efficiency of the Green's function in quantum many-body systems, especially for long-imaginary-time behavior, demonstrated on the polaron problem.

Contribution

It presents a novel Monte Carlo technique that applies the flat histogram principle to improve sampling in diagrammatic expansions without prior knowledge.

Findings

Superior accuracy in long-imaginary-time Green's function extraction

Effective sampling without prior information

Demonstrated on the polaron problem

Abstract

The diagrammatic Monte Carlo (Diag-MC) method is a numerical technique which samples the entire diagrammatic series of the Green's function in quantum many-body systems. In this work, we incorporate the flat histogram principle in the diagrammatic Monte method and we term the improved version "Flat Histogram Diagrammatic Monte Carlo" method. We demonstrate the superiority of the method over the standard Diag-MC in extracting the long-imaginary-time behavior of the Green's function, without incorporating any a priori knowledge about this function, by applying the technique to the polaron problem