New Functional Integral Approach to Strongly Correlated Fermi Systems: The Gutzwiller Approximation as a Saddle Point

We propose a new functional integral representation of the Hubbarda and Anderson models of lattice fermions. The simplest saddle-point approximation leads, at zero temperature, to the results derived from the Gutzwiller variational wave function. This approach uncovers the limitations of the Gutzwiller approximation and clarifies its connection to the "auxiliary-boson" mean-field theory of the Anderson model. This formulation leads to a novel strong-coupling mean-field theory which allows for a unified treatment of antiferromagnetism and ferromagnetism, metal-to-insulator transition, and Kondo compensation effects.