Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model

TL;DR

This paper develops a spin-rotational invariant Gutzwiller-based method to accurately compute magnetic excitations and susceptibilities in the Hubbard model, improving upon previous charge-focused approaches and aligning well with exact results.

Contribution

It introduces a time-dependent Gutzwiller theory for magnetic excitations that does not rely on assumptions about double occupancy dynamics, extending the GA+RPA framework to magnetic phenomena.

Findings

Accurately reproduces degeneracy of triplet excitations in spin-rotational systems.

Shows high accuracy compared to exact diagonalization results.

Predicts phase diagrams consistent with previous variational studies.

Abstract

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. {\bf 86}, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the double occupancy are needed in this case. Interestingly, in a spin-rotational invariant system, we find the correct degeneracy between triplet excitations, showing the consistency of both computations. Since no restrictions are imposed on the symmetry of the underlying saddle-point solution, our approach is suitable for the evaluation of the magnetic susceptibility and dynamical structure factor in strongly correlated inhomogeneous systems. We present a detailed study of the quality of our approach by comparing with exact diagonalization results and show its much higher accuracy compared to the conventional Hartree-Fock+RPA theory. In infinite dimensions, where the GA becomes exact for the Gutzwiller variational energy, we evaluate ferromagnetic and antiferromagnetic instabilities from the transverse magnetic susceptibility. The resulting phase diagram is in complete agreement with previous variational computations.