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We present a model example of a quantum critical behavior of renormalizedsingle-particle Wannier function composed of Slater s-orbitals and representedin an adjustable Gaussian STO-7G basis, which is calculated for cubic latticesin the Gutzwiller correlated state near the metal-insulator transition (MIT).The discussion is carried out within the extended Hubbard model and the methodof approach proposed earlier [cf. Eur. Phys. J. B {\bf 66}, 385 (2008)]. Thecomponent atomic-wave-function size, the Wannier function maximum, as well asthe 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 lawis interpreted as evidence of a dominant role of the interparticle Coulombrepulsion, which for $R>R_c$ is of intersite character. Relation of theinsulator-metal transition lattice-parameter value $R=R_{c}$ to the original{\em Mott criterion} is also obtained. The method feasibility is tested bycomparing our results with the exact approach for the Hubbard chain, for whichthe Mott-Hubbard transition is absent. In view of unique features of ourresults, an extensive discussion in qualitative terms is also provided.

the european physical journal. b, condensed matter physics/european physical journal. b, condensed matter and complex systems

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