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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

  • Solid State and Materials
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Abstract.

We present a model example of a quantum critical behavior of the 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 using the method of approach proposed earlier [Eur. Phys. J. B 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-Rc)/Rc] s with s in the interval [0.9, 1.0]. Such scaling law is interpreted as the evidence of a dominant role of the interparticle Coulomb repulsion, which for R > Rc is of intersite character. Relation of the insulator-metal transition critical value of the lattice-parameter 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.

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Authors and Affiliations

  1. Marian Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland

    J. Spałek & R. Podsiadły

  2. Faculty of Physics and Applied Computer Science, AGH Univ. of Science and Technology, Reymonta 19, 30-059, Kraków, Poland

    J. Spałek

  3. Institute of Physics, Cracow University of Technology, Podchorążych 1, 30-084, Kraków, Poland

    J. Kurzyk & W. Wójcik

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  1. J. Spałek
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Correspondence to J. Spałek.

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Spałek, J., Kurzyk, J., Podsiadły, R. et al. 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. Eur. Phys. J. B 74, 63–74 (2010). https://doi.org/10.1140/epjb/e2010-00077-6

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