Diagrammatic Monte Carlo

TL;DR

Diagrammatic Monte Carlo (DiagMC) is a numerical method for calculating many-body quantum properties using diagrammatic expansions, effectively managing the sign problem and providing new results for interacting fermion systems.

Contribution

This paper introduces DiagMC as a practical approach for many-body quantum calculations, including detailed methodology and initial results for the Hubbard model.

Findings

Effective management of the sign problem in DiagMC

First results for equations of state in the Hubbard model

Detailed description of DiagMC scheme for interacting fermions

Abstract

Diagrammatic Monte Carlo (DiagMC) is a numeric technique that allows one to calculate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem that is typically fatal to Monte Carlo approaches, appears to be manageable with DiagMC. Starting with a general introduction to the principles of DiagMC, we present a detailed description of the DiagMC scheme for interacting fermions (Hubbard model), as well as the first illustrative results for the equations of state.