Diagrammatic Monte Carlo for Correlated Fermions

TL;DR

This paper demonstrates that Diagrammatic Monte Carlo (DiagMC) can effectively solve challenging fermionic many-body problems in the thermodynamic limit, providing accurate results for the Hubbard model in the correlated Fermi liquid regime at moderate interaction strengths and low temperatures.

Contribution

The paper introduces the application of DiagMC to the Hubbard model, achieving accurate results in the thermodynamic limit for moderate interactions and low temperatures, which was previously challenging.

Findings

Accurate DiagMC results for the Hubbard model at U/t ~ 4

Study of temperatures down to T/t=1/40

Comparison with high temperature series and DMFT results

Abstract

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t \sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.