Some Remarks on the Gutzwiller Wave Function
The Gutzwiller variational wave function for the Hubbard model has seen a recent upsurge of interest(1,2,3,4). In this preliminary report, we present some analytical results for the variational energy. In Sec (A) we present the calculation of the energy in the ladder approximation, which is expected be exact for low particle density. Sec (B) contains an approximation equivalent to the Gutzwiller approximation (GA) to the calculation of the expectation value of the Hamiltonian with the help of a density matrix scheme, which appears to be the most streamlined rederivation available, and brings out the local nature of the approximation. In Sec (C) we focus on the 1/2 filled case and examine the possibility of a metal-insulator transition within the wave function. Sec (D) contains a simple exactly solvable model for which both the exact answer, and the variational calculation a la Gutzwiller are possible, and may shed some light on the possible singularities of the energy for the original problem.
Unable to display preview. Download preview PDF.