Critical scaling of the renormalized single-particle wave function near the Mott-Hubbard transition

We present a quantum critical behavior of the renormalized single-particle Wannier function, calculated in the Gutzwiller correlated state near the insulator-metal transition (IMT) for cubic lattices. The wave function size and its maximum, as well as the system energy scale with increasing lattice parameter $R$ as $R^{n}$. Such scaling is interpreted as the evidence of a dominant role of the Coulomb repulsion. Relation of the insulator-metal transition lattice-parameter value $R=R_{C}$ to the original {em Mott criterion} is obtained. The method is tested by comparing our results with the exact approach for the Hubbard chain.