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

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.

12 pages, 8 figures

References in corpus (8)

• Correlated Electrons in High Temperature Superconductors
• Metallic mean-field stripes, incommensurability and chemical potential in cuprates
• Time-dependent Gutzwiller approximation for the Hubbard model
• Unrestricted slave-boson mean-field approximation for the two-dimensional Hubbard model
• Dynamics of metallic stripes in cuprates
• Inhomogeneous Gutzwiller approximation with random phase fluctuations for the Hubbard model
• Properties of Gutzwiller wave-functions for multi-band models
• On the correct continuum limit of the functional-integral representation for the four-slave-boson approach to the Hubbard model: Paramagnetic phase

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