Brinkman-Rice transition in the three-band Hubbard model

Abstract

The ${\mathit{U}}_{\mathit{d}}$=\ensuremath{\infty} three-band Hubbard model on a two-dimensional ${\mathrm{CuO}}_{2}$ network is studied based on a Gutzwiller wave function by use of the variational Monte Carlo (VMC) method, where ${\mathit{U}}_{\mathit{d}}$ is the Coulomb repulsion between holes on the Cu site (hole picture). The VMC results are compared with those of the Rice-Ueda-type Gutzwiller approximation (GA) in a half-filled band, where the average number of holes per Cu site is n=1. In the GA the Brinkman-Rice (BR) transition occurs at a finite value of ${\mathrm{\ensuremath{\Delta}}}_{0}$=(${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{d}}$)/2, and then the number of d holes becomes ${\mathit{n}}_{\mathit{d}}$=n=1. Whether the BR transition really occurs or not within the Gutzwiller wave function is discussed in detail. In finite systems the absence of the BR transition is shown analytically. The thermodynamic limit is examined assuming the asymptotic behavior of ${\mathit{n}}_{\mathit{d}}$ is given by a scaling function. The results of the finite-size scaling analysis suggest the absence of the BR transition as that in the single-band Hubbard model.