Dual fermion method as a prototype of generic reference-system approach for correlated fermions

TL;DR

This paper provides a diagrammatic derivation of the dual fermion method, demonstrating its applicability to arbitrary reference systems with the same interaction, and shows its effectiveness on the 2D Hubbard model with results aligning well with quantum Monte Carlo data.

Contribution

It introduces a general diagrammatic derivation of the dual fermion scheme applicable to any reference system with identical interactions, expanding its versatility.

Findings

Results agree well with quantum Monte Carlo data for the 2D Hubbard model.

The derivation clarifies the role of the dual denominator in the self-energy expression.

The method is applicable beyond local reference systems, including non-lattice systems.

Abstract

We present a purely diagrammatic derivation of the dual fermion scheme [Phys. Rev. B 77 (2008) 033101]. The derivation makes particularly clear that a similar scheme can be developed for an arbitrary reference system provided it has the same interaction term as the original system. Thereby no restrictions are imposed by the locality of the reference problem or by the nature of the original problem as a lattice one. We present new arguments in favour of keeping the dual denominator in the expression for the lattice self-energy independently of the truncation of the dual interaction. As an example we present the computational results for the half-filled 2D Hubbard model with the choice of a $2\times2$ plaquette with periodic boundary conditions as a reference system. We observe that obtained results are in a good agreement with numerically exact lattice quantum Monte Carlo data.