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

Abstract

We present a model example of a quantum critical behavior of 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 the method of approach proposed earlier [cf. Eur. Phys. J. B {\bf 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 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 lattice-parameter value $R=R_c$ to the original {\em 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.

17 pages, 12 figures, 2 tables, 2 appendixes

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• The Mott criterion: So simple and yet so complex