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arXiv:0801.4528 · Physical Review B

Slave-boson based configuration-interaction approach for the Hubbard model

G. Seibold

Published Jun 12, 2008• 3 citations
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Abstract

Based on the Kotliar--Ruckenstein slave-boson scheme, we develop a configuration-interaction (CI) approach that is suitable to evaluate energy corrections for symmetry-broken saddle-point solutions. The theory is applied to spin-polaron states in the Hubbard model and compared with analogous results obtained within the Hartree--Fock approximation. In addition, we show that within the infinite $\mathcal{D}$ prescription of the Gutzwiller method a CI approach does not correct the variational result since in the thermodynamic limit matrix elements between different inhomogeneous states vanish due to an ``orthogonality catastrophe.''

DOI
10.1103/physrevb.77.235109

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Based on the Kotliar--Ruckenstein slave-boson scheme, we develop a configuration-interaction (CI) approach that is suitable to evaluate energy corrections for symmetry-broken saddle-point solutions. The theory is applied to spin-polaron states in the Hubbard model and compared with analogous results obtained within the Hartree--Fock approximation. In addition, we show that within the infinite D\mathcal{D}D prescription of the Gutzwiller method a CI approach does not correct the variational result since in the thermodynamic limit matrix elements between different inhomogeneous states vanish due to an ``orthogonality catastrophe.''
The Kotliar-Ruckenstein slave-boson scheme is used to allow for an unrestricted variation of the bosonic and fermionic fields on the saddle-point level. Various inhomogeneous solutions, such as spin polarons and domain walls, are discussed within the two-dimensional Hubbard model and compared with results of unrestricted Hartree-Fock (HF) calculations. We find that the present approach drastically reduces the polarization of these states and leads to increased delocalized wave functions as compared to the HF model. The interaction between two spin polarons turns out to be attractive over a wide range of the on-site repulsion UUU. In addition we obtain the crossover from vertical to diagonal domain walls at a higher value of UUU than predicted by HF.
We consider slave boson formulations of the Hubbard model, the t–J model and the Anderson model, in which spin and charge fermion degrees of freedom are represented by Bose fields. The approach has been applied to the Hubbard model generalizing the formulation of Kotliar and Ruckenstein. There the Gutzwiller solution is recovered as a saddle point. The method allows to find other types of mean field solutions in a systematic way. Dynamical correlation functions in mean field approximation as well as fluctuation contributions are also calculated.
The one-band Hubbard model is considered in the slave-boson formulation first introduced by Kotliar and Ruckenstein. It is shown that a mean-field approximation, where broken-symmetry states appropriate for a bipartite lattice are allowed, leads to a quantitative agreement with quantum Monte Carlo results for local observables over a wide range of interactions (0U\ensuremath{\le}20t) and doping (0n〉\ensuremath{\le}1). Thus, our saddle-point solutions constitute an excellent starting point for a systematic treatment of fluctuations.
We revisit the Kotliar-Ruckenstein (KR) slave boson saddle point evaluation for a two-site correlated electron model. As the model can be solved analytically, it is possible to compare the KR saddle point results with the exact many-particle levels. The considered two-site cluster mimics an infinite-UUU single-impurity Anderson model with a nearest-neighbor Coulomb interaction: one site is strongly correlated with an infinite local Coulomb repulsion, which hybridizes with the second site, on which the local Coulomb repulsion vanishes. Making use of the flexibility of the representation, we introduce appropriate weight factors in the KR saddle point scheme. Ground-state and all excitation levels agree with the exact diagonalization results. Thermodynamics and correlation functions may be recovered in a suitably renormalized saddle point evaluation.
We present a slave-boson representation for the Hubbard model, introducing Bose fields for the empty, singly, and doubly occupied sites and show that the boson for the singly occupied site must transform as a tensor of rank two under spin rotations. This generalizes the formulation of Kotliar and Ruckenstein, which is not manifestly spin-rotation invariant. The paramagnetic saddle point of the corresponding functional integral is identical to Gutzwiller's solution. As an illustration of the method, we calculate the T3{T}^{3}T3lnT spin-fluctuation contribution to the specific heat and find it to be fully consistent with Fermi-liquid theory. We discuss further applications of this approach.