Eur. Phys. J. B (2013) 86: 252
https://doi.org/10.1140/epjb/e2013-40127-y

Regular Article

Extended Hubbard model with renormalized Wannier wave functions in the correlated state III

Statistically consistent Gutzwiller approximation and the metallization of atomic solid hydrogen

¹ Marian Smoluchowski Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
² Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, ul. Reymonta 19, 30-059 Kraków, Poland
³ Institute of Physics, Kraków University of Technology, Podchorążych 1, 30-084 Kraków, Poland

^a e-mail: ufspalek@if.uj.edu.pl

Received: 14 February 2013
Received in final form: 15 April 2013
Published online: 6 June 2013

Abstract

We extend our previous approach [J. Kurzyk, W. Wójcik, J. Spalek, Eur. Phys. J. B 66, 385 (2008); J. Spałek, J. Kurzyk, R. Podsiadły, W. Wójcik, Eur. Phys. J. B 74, 63 (2010)] to modeling correlated electronic states and the metal-insulator transition by applying the so-called statistically consistent Gutzwiller approximation (SGA) to carry out self-consistent calculations of the renormalized single-particle Wannier functions in the correlated state. The transition to the Mott-Hubbard insulating state at temperature T = 0 is of weak first order even if antiferromagnetism is disregarded. The magnitude of the introduced self-consistent magnetic correlation field is calculated and shown to lead to a small magnetic moment in the magnetically uniform state. Realistic value of the applied magnetic field has a minor influence on the metallic-state characteristics near the Mott-Hubbard localization threshold. The whole analysis has been carried out for an extended Hubbard model on a simple cubic (SC) lattice and the evolution of physical properties is analyzed as a function of the lattice parameter for the renormalized 1s-type Wannier functions. Quantum critical scaling of the selected physical properties is analyzed as a function of the lattice constant R → R_c = 4.1a₀, where R_c is the critical value for metal-insulator transition and a₀ = 0.53 Å is the Bohr radius. A critical pressure for metallization of solid atomic hydrogen is estimated and is ~10² GPa.