Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions

TL;DR

This paper develops a Dual Fermion method to compute the two-particle Green function and susceptibility in strongly correlated lattice systems, capturing non-local correlations and predicting antiferromagnetic instability.

Contribution

It introduces a practical scheme for calculating susceptibilities within the Dual Fermion framework, including Bethe-Salpeter equations and an approximation, applied to the 2D Hubbard model.

Findings

Susceptibility increases at wavevector (π,π), indicating antiferromagnetic instability.

Non-local spin fluctuations suppress the critical temperature compared to mean-field predictions.

The method effectively captures non-local correlations in strongly correlated systems.

Abstract

In this paper, we show how the two-particle Green function (2PGF) can be obtained within the framework of the Dual Fermion approach. This facilitates the calculation of the susceptibility in strongly correlated systems where long-ranged non-local correlations cannot be neglected. We formulate the Bethe-Salpeter equations for the full vertex in the particle-particle and particle-hole channels and introduce an approximation for practical calculations. The scheme is applied to the two-dimensional Hubbard model at half filling. The spin-spin susceptibility is found to strongly increase for the wavevector $\vc{q}=(\pi,\pi)$, indicating the antiferromagnetic instability. We find a suppression of the critical temperature compared to the mean-field result due to the incorporation of the non-local spin-fluctuations.