Effective Field and Metal—Insulator Phase Transition in the Hubbard Model

E. E. Zubov$^{1,2}$

$^{1}$G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03680 Kyiv-142, Ukraine
$^{2}$Vasyl Stus Donetsk National University, 21 600-Richchya Str., 21021 Vinnytsia, Ukraine

In the framework of the Hubbard model with an effective self-consistent field, a possible mechanism of the stepwise metal–insulator phase transition for a half-filled band is presented. A detailed investigation of the well-known Hubbard-I approximation is carried out. In addition, the correlation corrections are accounted with a minimal number of self-consistency parameters. As determined, the typical order parameters are unique for a metal state or a dielectric one. Based on analysis of the electron spectral density, the position of the chemical-potential level and the critical value of Coulomb repulsion energy in bandwidth units at the metal–insulator phase transition are determined. The estimations of the internal-energy value for a half-filled band show a stable metal state at $\tilde{U} < 2.1$. A dielectric state is stable for $\tilde{U} >2.1$ and only in the limit of the extremely small electron doping. That is why the chemical-potential level underlies by lower edge of the upper Hubbard band where the spectral density is equal to zero. It gives zero conductivity. The finite electron or hole dopings cause the metal state with Fermi level inside the upper band or the doped dielectric state with Fermi level inside the lower band, respectively. It results in a stepwise increasing of conductivity at the metal–insulator phase transition.

Key words: metal, insulator, phase transition, conductivity, chemical potential.

URL: http://mfint.imp.kiev.ua/en/abstract/v38/i11/1423.html

DOI: https://doi.org/10.15407/mfint.38.11.1423

PACS: 71.10.Fd, 71.10.Hf, 71.20.Be, 71.27.+a, 71.30.+h, 72.15.Eb, 72.60.+g

Citation: E. E. Zubov, Effective Field and Metal—Insulator Phase Transition in the Hubbard Model, Metallofiz. Noveishie Tekhnol., 38, No. 11: 1423—1446 (2016) (in Russian)

REFERENCES
1. J. Hubbard, Proc. Roy. Soc. Lond. A, 276: 238 (1963). Crossref
2. J. Hubbard, Proc. Roy. Soc. Lond. A, 281: 401 (1964). Crossref
3. Yu. A. Yzyumov, Uspekhi Fizicheskikh Nauk, 167, No. 5: 465 (1997) (in Russian).
4. M. J. Rozenberg, G. Kotliar, and X. Y. Zhang, Phys. Rev. B, 49, No.15: 10181 (1994). Crossref
5. N. F. Mott, Metal-Insulator Transitions (London: Taylor&Francis: 1990).
6. W. F. Brinkman and T. M. Rice, Phys. Rev. B, 7, No. 4: 1508 (1973). Crossref
7. R. O. Zaitsev, Sov. Phys. JETP, 48, No.6: 1193 (1978).
8. Yu. A. Izyumov and Yu. N. Skryabin, Statisticheskaya Mekhanika Magnitouporyadochennikh System [Statistical Mechanics of the Magnetically Ordered Systems] (Moscow: Nauka: 1987) (in Russian).
9. E. E. Zubov, Physica C, 497: 67 (2014). Crossref
10. T. Morita and T. Horiguchi, J. Math. Phys., 12, No. 6: 986 (1971). Crossref
11. G. S. Joyce Phil. Trans. R. Soc. Lond. A, 273: 583 (1973). Crossref
12. T. Morita and T. Horiguchi, Numer. Math., 20: 425 (1973). Crossref
13. O. K. Kalashnikov and E. S. Fradkin, Teoreticheskaya i Matematicheskaya Fizika, 5, No. 3: 417 (1970) (in Russian).
14. D. M. Edwards, A. C. M. Green, and K. Kubo, J. Phys.: Condens. Matter., 11: 2791 (1999). Crossref