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International Journal of Modern Physics B

Unified Slave Boson Representation of Spin and Charge Degrees of Freedom for Strongly Correlated Fermi Systems

Raymond Frésard, P. Wölfle

Published Mar 1, 1992• 108 citations
Publisher

Abstract

We consider a slave boson representation of lattice electrons in terms of bosons for the empty, singly and doubly occupied site. The approach generalizes an earlier formulation by Kotliar and Ruckenstein. As examples the Hubbard model and the t-J model are considered. The emphasis is on a detailed derivation and discussion of the formal aspects. Simple meanfield solutions are discussed for illustrative purposes.

DOI
10.1142/s0217979292000414

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We consider a slave boson representation of lattice electrons in terms of bosons for the empty, singly and doubly occupied site. The approach generalizes an earlier formulation by Kotliar and Ruckenstein. As examples the Hubbard model and the t-J model are considered. The emphasis is on a detailed derivation and discussion of the formal aspects. Simple meanfield solutions are discussed for illustrative purposes.
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.
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 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.
The grand canonical system of hard-core bosons, subject to thermal fluctuations, is studied on a lattice. Starting from the slave-boson representation we derive an effective Ginzburg-Landau functional for the superfluid order parameter. The order parameter field is a collective field constructed from the slave-boson fields for empty and singly occupied sites. We find two phase transitions; one from a normal fluid at high density to a superfluid and another one from the superfluid to a normal fluid at low density.
We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model, where it systematically overestimates the importance of electronic correlation effects for weak interaction strength, by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.