Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime

TL;DR

This paper introduces a numerically exact Diagrammatic Determinant Monte Carlo method to sum irreducible Feynman diagrams for fermionic self-energy, enabling detailed analysis of strongly correlated systems like the 2D Hubbard model.

Contribution

It extends the Diagrammatic Determinant Monte Carlo technique to high-order connected diagrams, allowing controlled reconstruction of the self-energy in strongly correlated regimes.

Findings

Achieved high-order expansions (~10) for the 2D Hubbard model.

Revealed non-trivial analytic structure of the self-energy.

Enabled momentum-resolved analysis in the nonperturbative regime.

Abstract

We develop a numerically exact method for the summation of irreducible Feynman diagrams for fermionic self-energy in the thermodynamic limit. The technique, based on the Diagrammatic Determinant Monte Carlo and its recent extension to connected diagrams, allows us to reach high ($\sim 10$) orders of the weak-coupling expansion for the self-energy of the two-dimensional Hubbard model. Access to high orders reveals a non-trivial analytic structure of the self-energy and enables its controlled reconstruction with arbitrary momentum resolution in the nonperturbative regime of essentially strong correlations, which has recently been reached with ultracold atoms in optical lattices.