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International Journal of Modern Physics B

SPIN-CARRYING SLAVE BOSON REPRESENTATION FOR STRONGLY CORRELATED FERMION SYSTEMS

P. Wölfle

Published Dec 1, 1989• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979289001172

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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.
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.
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 review the slave-boson representations of the Hubbard model. When both spin and charge fermion degrees of freedom are represented by Bose fields, the approach is equivalent at the "self-consistent" saddle point level to the Gutzwiller approximation (GA). We show how the determination of the Lagrange multipliers, introduced to enforce the constraints, involves a Mott-Hubbard gap near half-filling for U > U c (localization edge). The quantum fluctuations are then considered within a renormalized basis of boson fields (restoring the spin-rotation invariance), which brings out two distinct channels, symmetric and antisymmetric. It is remarkable that both spin and charge fluctuations are obtained at the same level of the gaussian fluctuations, as oppossed to the standard 1/N expansion. This provides the microscopic basis for a Fermi liquid theory. Both dynamic effects and extension to finite temperature which were beyond the scope of the variational procedure can now be described by this approach. The physical implications of the model (dynamic correlation functions, T3Ln T term of the specific heat, superfluid instability) are finally considered, all of which reflect the Fermi liquid nature of the system.
We determine the free energy of strongly correlated electron systems in the example of the Hubbard model by calculating the contribution of spin and charge fluctuations to the Gutzwiller approximation mean-field result. We employ the slave-boson formulation of Kotliar and Ruckenstein in its spin-rotation-invariant form in the usual continuous-time approximation of the functional integral representation, corrected by “high-frequency contributions” ( SRIKR + ). In contrast to all previous attempts to calculate the fluctuation contribution to the free energy within the spin-rotation-invariant Kotliar-Ruckenstein slave-boson representation (SRIKR) scheme our result preserves the noninteracting limit. We show that the correct form of the kinetic energy renormalization is essential. The results for the ground-state energy in the paramagnetic phase are in very good agreement with state-of-the-art results obtained by methods such as density matrix embedding theory, quantum Monte Carlo, and others. The leading low-temperature behavior of the free energy allows us to extract the quasiparticle effective mass, in particular its enhancement near a continuous phase transition into an ordered state. Our work demonstrates that the SRIKR + method is competitive with the best available alternative methods and equips the slave-boson approach with an improved synoptic power to explore strongly correlated electron systems.