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

TL;DR

This paper investigates the quantum critical behavior of renormalized Wannier functions near the Mott-Hubbard transition in the extended Hubbard model, revealing scaling laws and the role of Coulomb interactions in the metal-insulator transition.

Contribution

It introduces a model of Wannier function scaling near the MIT, incorporating Coulomb interactions, and relates the transition point to the Mott criterion within the extended Hubbard framework.

Findings

Wannier function size scales as [(R-R_c)/R_c]^s with s in [0.9,1.0]

System energy and Wannier maximum exhibit similar scaling behavior

Relation established between R_c and the Mott criterion

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.