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arXiv:0803.4051 · Physical Review B

Time-dependent Gutzwiller theory of pairing fluctuations in the Hubbard model

G. Seibold, Federico Becca, J. Lorenzana

Published Jul 23, 2008• 16 citations
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Abstract

We present a method to compute pairing fluctuations on top of the Gutzwiller approximation (GA). Our investigations are based on a charge-rotational invariant GA energy functional which is expanded up to second order in the pair fluctuations. Equations of motion for the fluctuations lead to a renormalized ladder-type approximation. Both spectral functions and corrections to static quantities, such as the ground-state energy, are computed. The quality of the method is examined for the single-band Hubbard model, where we compare the dynamical pairing correlations for $s$- and $d$-wave symmetries with exact diagonalizations. We find a significant improvement with respect to analogous calculations done within the standard Hartree-Fock ladder approximation. The technique has potential applications in the theory of Auger spectroscopy, superconductivity, and cold atom physics.

DOI
10.1103/physrevb.78.045114

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We present a method to compute pairing fluctuations on top of the Gutzwiller approximation (GA). Our investigations are based on a charge-rotational invariant GA energy functional which is expanded up to second order in the pair fluctuations. Equations of motion for the fluctuations lead to a renormalized ladder-type approximation. Both spectral functions and corrections to static quantities, such as the ground-state energy, are computed. The quality of the method is examined for the single-band Hubbard model, where we compare the dynamical pairing correlations for sss- and ddd-wave symmetries with exact diagonalizations. We find a significant improvement with respect to analogous calculations done within the standard Hartree-Fock ladder approximation. The technique has potential applications in the theory of Auger spectroscopy, superconductivity, and cold atom physics.
We develop a time-dependent Gutzwiller approximation (GA) for the Hubbard model analogous to the time-dependent Hartree-Fock (HF) method. This new formalism incorporates ground state correlations of the random phase approximation (RPA) type beyond the GA. Static quantities like ground state energy and double occupancy are in excellent agreement with exact results in one dimension up to moderate coupling and in two dimensions for all couplings. We find a substantial improvement over traditional GA and HF+RPA treatments. Dynamical correlation functions can be computed and are also substantially better than HF+RPA ones and obey well behaved sum rules.
We present a detailed study of the time-dependent Gutzwiller approximation for the Hubbard model. The formalism, labeled 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.
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\mathrm{GA}+\mathrm{RPA}GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. 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 $\mathrm{Hartree}\ensuremath{-}\mathrm{Fock}+\mathrm{RPA}$ 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.
The description of electronic inhomogeneities in transition metal compounds requires a technique which is able to deal with the excitations of an inhomogeneous, strongly correlated system. In this talk I will outline the formalism of the timedependent Gutzwiller approximation [1] for the Hubbard model which allows for the computation of random phase approximation (RPA) like fluctuations on top of the Gutzwiller approximation (GA). The performance of the method is demonstrated by comparing static quantities like ground state energy and double occupancies as well as dynamical correlation functions in the charge, spin and pair channels with HartreeFock+RPA and exact results. I will further show that the method gives a good account of several spectroscopic quantities related to stripes in highTc superconductors. A major part of the talk will address the recent generalization of the method to the case of multiple bands [2,3]. Contrary to the standard RPA, the incorporation of the local multipletstructure within our approach leads to a much larger sensitivity of ferromagnetism on the the ratio between Hund coupling and intraorbital repulsion J/U. Besides, we find that the Brinkman Rice localization transition, which in the paramagnetic GA appears at integer doping is always masked by an antiferromagnetic or an orbitally ordered ground state. In addition, a quantum Lifshitz point is found at larger values of J/U which corresponds to the common boundary of ferro, para and incommensurate magnetic phases. [1] G. Seibold and J. Lorenzana, Phys. Rev. Lett. 86, 2605 (2001) [2] E. von Oelsen, G. Seibold, and J. Bunemann, New J. Phys. 13, 113031 (2011) [3] E. v. Oelsen, G. Seibold, and J. Bunemann, Phys. Rev. Lett. 107, 076402 (2011)
We formulate a multi-band generalization of the time-dependent Gutzwiller theory. This approach allows for the calculation of general two-particle response functions, which are crucial for an understanding of various experiments in solid-state physics. As a first application, we study the momentum- and frequency-resolved magnetic susceptibility in a two-band Hubbard model. As in the case of underlying ground-state approaches, we find significant differences between the results of our method and those from a time-dependent Hartree–Fock approximation.