Inhomogeneous Gutzwiller approximation with random phase fluctuations for the Hubbard model

TL;DR

This paper develops an advanced time-dependent Gutzwiller approximation method, GA+RPA, to accurately compute linear excitations in the Hubbard model, outperforming traditional Hartree-Fock based approaches.

Contribution

The paper introduces the GA+RPA formalism for the Hubbard model, enabling fluctuation calculations without symmetry restrictions and demonstrating improved accuracy over HF+RPA.

Findings

GA+RPA obeys sum rules similar to HF+RPA

Analytical and numerical results show better performance than HF+RPA

Supports calculations of charge and current fluctuations in low dimensions

Abstract

We present a detailed study of the time-dependent Gutzwiller approximation for the Hubbard model. The formalism, labelled GA+RPA, allows us to compute random-phase approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). No restrictions are imposed on the charge and spin configurations which makes the method suitable for the calculation of linear excitations around symmetry-broken solutions. Well-behaved sum rules are obeyed as in the Hartree-Fock (HF) plus RPA approach. Analytical results for a two-site model and numerical results for charge-charge and current-current dynamical correlation functions in one and two dimensions are compared with exact and HF+RPA results, supporting the much better performance of GA+RPA with respect to conventional HF+RPA theory.