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

• Published in: arXiv.org
• Main Authors: Spałek, Jozef, Kurzyk, Jan, Podsiadły, Robert, Wójcik, Włodzimierz
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 09.12.2009
• Subjects: Insulators; Lattices; Metal-insulator transition; Parameters; Physics - Strongly Correlated Electrons; Scaling laws; Wave functions
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0912.0915

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.