Extended Hubbard model with the 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 66, 385 (2008)]. The component atomic-wavefunction size, the Wannier function maximum, as well as the system energy, all scale with the increasing lattice parameter R as [(R − Rc)/Rc] 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 > Rc is of intersite character. Relation of the insulator-metal transition lattice-parameter value R = Rc to the original 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.

Discontinuous transition of molecular-hydrogen chain to the quasiatomic state: Combined exact diagonalization andab initioapproach

“…Parenthetically, note that we have neglected the direct exchange interaction and the so-called correlated-hopping terms [25], as they are of much smaller amplitude at these distances. Note also that the Mott criterion at the transition [26,27] takes in the present situation the form a B n 1/d C ≡ (αa) −1 ≈ 0.45 at the transition, not too far from the value 0.25 for 3dimensional (d = 3) systems.…”

“…We think that tackling of this problem is possible on a small scale within our Exact Diagonalization Ab Initio (EDABI) approach employed here and to other problems [29] involving electronic correlations as an essential aspect of their physical properties. For 3d system, approximate second-quantization diagonalization schemes such as the statistically-consistent Gutzwiller approximation may be used with concomitant single-particle wave-function optimization [27]. These methods can be tested in the present exact limit.…”

On the Problem of Metal-Insulator Transitions in Vanadium Oxides

“…Generally, expressions of the type D = (where is the electron localization radius, for instance, B ) or = (where and are the kinetic and potential electron energies, resp.) are nearly equivalent to the Mott criterion given by (1): see, for example, discussions in the works [12,20] related to this issue. Note that the value of B is determined by the dielectric constant and effective mass.…”

Metallization of Atomic Solid Hydrogen within the Extended Hubbard Model with Renormalized Wannier Wave Functions

“…We start with the extended Hubbard Hamiltonian describing a single-band hydrogen system [10][11][12] :…”

“…In the series of papers [10][11][12] , we have conducted model calculations combining both the Mott 5 and the Hubbard 13 aspects of the phase transition, within the extended Hubbard model, with a simultaneous renormalization of the single-particle Wannier basis, connecting first-and second-quantization approach. In 12 we obtained, using proposed model, the critical metallization pressure p C = 97.7 GP a required to stabilize the atomic-hydrogen-like crystal, while having both the Mott (n 1/3 C a B ≈ 0.2) and the Hubbard (U ≈ W ) criteria satisfied at the same time.…”