Diagrammatic Monte Carlo for Dual Fermions

TL;DR

This paper presents a stochastic algorithm for sampling dual fermion perturbation series, enabling systematic inclusion of non-local correlations in strongly correlated materials, with rapid convergence in weak coupling and significant corrections in strong coupling regimes.

Contribution

The paper introduces a novel diagrammatic Monte Carlo method for dual fermions that efficiently captures non-local correlations beyond dynamical mean field theory.

Findings

Method converges quickly in weak coupling regime.

Large corrections observed in strong correlation regime.

Low-frequency propagators dominate the diagrams.

Abstract

We introduce a numerical algorithm to stochastically sample the dual fermion perturbation series around the dynamical mean field theory, generating all topologies of two-particle interaction vertices. We show results in the weak and strong coupling regime of the half-filled Hubbard model in two dimensions, illustrating that the method converges quickly where dynamical mean field theory is a good approximation, and show that corrections are large in the strong correlation regime at intermediate interaction. The fast convergence of dual corrections to dynamical mean field results illustrates the power of the approach and opens a practical avenue towards the systematic inclusion of non-local correlations in correlated materials simulations. An analysis of the frequency scale shows that only low-frequency propagators contribute substantially to the diagrams, putting the inclusion of higher order vertices within reach.