Lattice susceptibility for 2D Hubbard Model within dual fermion method

TL;DR

This paper develops and applies the dual fermion method to compute lattice susceptibility in the 2D Hubbard model, comparing results with quantum Monte Carlo and dynamical vertex approximation methods.

Contribution

It provides a detailed implementation of the dual fermion approach for susceptibility calculations and compares its results with other advanced methods.

Findings

Dual fermion method captures magnetic instability in 2D Hubbard model.

Lattice susceptibility results agree well with QMC simulations.

Comparison shows strengths of dual fermion over other methods in certain regimes.

Abstract

In this paper, we present details of the dual fermion (DF) method to study the non-local correction to single site DMFT. The DMFT two-particle Green's function is calculated using continuous time quantum monte carlo (CT-QMC) method. The momentum dependence of the vertex function is analyzed and its renormalization based on the Bethe-Salpeter equation is performed in particle-hole channel. We found a magnetic instability in both the dual and the lattice fermions. The lattice fermion susceptibility is calculated at finite temperature in this method and also in another recently proposed method, namely dynamical vertex approximation (D$\Gamma$A). The comparison between these two methods are presented in both weak and strong coupling region. Compared to the susceptibility from quantum monte carlo (QMC) simulation, both of them gave satisfied results.