Linear Response Functions Respecting Ward-Takahashi Identity and Fluctuation-Dissipation Theorem within $GW$ Approximation

TL;DR

This paper introduces a self-consistent GW-based method for calculating response functions in correlated electronic systems that respects both the Ward-Takahashi identity and the fluctuation-dissipation theorem, verified on a Hubbard model.

Contribution

It presents a novel GW-based approach that ensures physical consistency of response functions while reducing computational costs compared to Monte Carlo methods.

Findings

Method accurately reproduces spin susceptibility results.

Verifies Ward-Takahashi identity and fluctuation-dissipation theorem numerically.

Achieves computational efficiency in response function calculations.

Abstract

The calculation of response functions in correlated electronic systems is one of the most important problems in the condensed matter physics. To obtain a physical response function, preserving both the Ward-Takahashi identity and the fluctuation-dissipation theorem are crucial. Here we propose a self-consistent many body method within the GW framework to calculate the response functions based on the fluctuation-dissipation theorem, which also satisfies the Ward-Takahashi identity. The validity of this methodology is demonstrated on the two-dimensional one-band Hubbard model, where both the Ward-Takahashi identity and fluctuation-dissipation theorem are verified numerically. Moreover, comparing to the accurate spin susceptibility of the determinantal Monte Carlo approach, the results obtained from our method are quite satisfactory and the computational cost are greatly reduced.