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Physical review. B, Condensed matter

Spin- and charge-rotation invariant approach to the Hubbard model

J. J. Vicente Alvarez, C. A. Balseiro, Hermenegildo Alejandro Ceccatto

Published Oct 15, 1996• 11 citations
Publisher

Abstract

We present a slave-boson formulation for the Hubbard model that preserves the spin-rotation and particle-hole symmetries of the paramagnetic phase at half filling. Fermion and boson fields are treated on an equal footing in a functional integral formulation. We show that, while in two and three dimensions there is a metal-insulator transition as the interaction U increases, in one dimension our approach always gives an insulating state. Short-range spin-spin correlations are included at the saddle-point level for all values of U, giving a good description of the insulating state. We show that the energy gap in the one-particle spectrum increases from zero as (U-${\mathit{U}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{\alpha}}}$, where ${\mathit{U}}_{\mathit{c}}$ is the critical value of the on-site interaction and the exponent \ensuremath{\alpha} is 1 and 1/2 for 2 and 3 dimensions, respectively. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.11207

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A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy DDD. Its saddle-point mean-field theory is equivalent to the Gutzwiller approximation, as in the case of single-band Hubbard model. Our theory is applied to the doubly degenerate (D=2D = 2D=2) model, and numerical calculations have been performed for this model in the paramagnetic states. The effect of the exchange interaction on the metal-insulator (MI) transition is discussed. The critical interaction for the MI transition is analytically calculated as functions of orbital degeneracy and electron occupancy.
The authors determine the ground-state phase diagram of the Hubbard model on the square lattice allowing for homogeneous spiral, antiferromagnetic, ferromagnetic and paramagnetic phases in the overall parameter range. This is obtained from a saddle-point approximation of a spin-rotation-invariant form of the slave-boson representation introduced by Kotliar and Ruckenstein (1986). In addition they determine analytically the transition point for infinite repulsive interaction strength between the Nagaoka state and the paramagnetic state on any bipartite lattice.