Eur. Phys. J. B 74, 63-74 (2010)
https://doi.org/10.1140/epjb/e2010-00077-6

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

¹ Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
² Faculty of Physics and Applied Computer Science, AGH Univ. of Science and Technology, Reymonta 19, 30-059 Kraków, Poland
³ Institute of Physics, Cracow University of Technology, Podchorążych 1, 30-084 Kraków, Poland

Corresponding author: ufspalek@if.uj.edu.pl

Received: 26 November 2009
Revised: 26 January 2010
Published online: 2 March 2010

Abstract

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.