Extended Hubbard model with the renormalized Wannier wave functions in the correlated state II: quantum critical scaling of the wave function near the Mott-Hubbard transition

We present a model example of a quantum critical behavior of the renormalized single-particle Wannier function composed of Slater s-orbitals and represented in an adjustable Gaussian STO-7G basis, which is calculated for cubic lattices in the Gutzwiller correlated state near the metal-insulator transition (MIT). The discussion is carried out within the extended Hubbard model and using the method of approach proposed earlier [Eur. Phys. J. B 66, 385 (2008)]. The component atomic-wave-function size, the Wannier function maximum, as well as the system energy, all scale with the increasing lattice parameter R as [ (R-R c)/R c] s with s in the interval [0.9, 1.0]. Such scaling law is interpreted as the evidence of a dominant role of the interparticle Coulomb repulsion, which for R > R c is of intersite character. Relation of the insulator-metal transition critical value of the lattice-parameter R=R c to the original Mott criterion is also obtained. The method feasibility is tested by comparing our results with the exact approach for the Hubbard chain, for which the Mott-Hubbard transition is absent. In view of unique features of our results, an extensive discussion in qualitative terms is also provided. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010