Abstract.
The Mott-Hubbard metal-insulator transition is investigated in a two-band Hubbard model within dynamical mean-field theory. To this end, we use a suitable extension of Wilson’s numerical renormalization group for the solution of the effective two-band single-impurity Anderson model. This method is non-perturbative and, in particular, allows to take into account the full exchange part of the Hund’s rule coupling between the two orbitals. We discuss in detail the influence of the various Coulomb interactions on thermodynamic and dynamic properties, for both the impurity and the lattice model. The exchange part of the Hund’s rule coupling turns out to play an important role for the physics of the two-band Hubbard model and for the nature of the Mott-transition.
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References
M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)
J. Hubbard, Proc. R. Soc. London A 276, 238 (1963); M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963); J. Kanamori, Prog. Theor. Phys. 30, 275 (1963)
W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)
T. Pruschke, M. Jarrell, J.K. Freericks, Adv. Phys. 42, 187 (1995)
A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
M. Jarrell, Th. Pruschke, Z. Phys. B 90, 187 (1993)
R. Bulla, Phys. Rev. Lett. 83, 136 (1999)
R. Bulla, T.A. Costi, D. Vollhardt, Phys. Rev. B 64, 045103 (2001)
D.B. McWhan, J.P. Remeika, Phys. Rev. B 2, 3734 (1970); D.B. McWhan et al., Phys. Rev. B 7, 1920 (1973)
M.J. Rozenberg et al., Phys. Rev. Lett. 75, 105 (1995)
P. Limelette, A. Georges, D. Jérome, P. Wzietek, P. Metcalf, J.M. Honig, Science 302, 89 (2003)
C. Castellani, C.R. Natoli, J. Ranninger, Phys. Rev. B 18, 4967 (1978); C. Castellani, C.R. Natoli, J. Ranninger, Phys. Rev. B 18, 5001 (1978)
S. Yu. Ezhov, V.I. Anisimov, D.I. Khomskii, G.A. Sawatzky, Phys. Rev. Lett. 83, 4136 (1999)
M.J. Rozenberg, Phys. Rev. B 55, R4855 (1997)
J.E. Han, M. Jarrell, D.L. Cox, Phys. Rev. B 58, 4100 (1998)
A. Koga, Y. Imai, N. Kawakami, Phys. Rev. B 66, 165107 (2002)
S. Florens, A. Georges, G. Kotliar, O. Pacollet, Phys. Rev. B 66, 205102 (2002)
Y. Ōno, M. Potthoff, R. Bulla, Phys. Rev. B 67, 035119 (2003)
G. Kotliar, D. Vollhardt, Physics Today 57, No. 3 (March), 53 (2004); K. Held, I.A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A.K. McMahan, R.T. Scalettar, Th. Pruschke, V.I. Anisimov, D. Vollhardt, Psi-k Newsletter #56, 65 (2003) [psi-k.dl.ac.uk/ newsletters/News_56/Highlight_56.pdf]
S. Sakai, R. Arita, H. Aoki, Phys. Rev. B 70, 172504 (2004)
A.N. Rubtsov, V.V. Savkin, A.I. Lichtenstein, cond-mat/0411344 (2004)
K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975); H.R. Krishna-Murthy, J.W. Wilkins, K.G. Wilson, Phys. Rev. B 21, 1003 (1980); H.R. Krishna-Murthy, J.W. Wilkins, K.G. Wilson, Phys. Rev. B 21, 1044 (1980)
R. Bulla, A.C. Hewson, Th. Pruschke, J. Phys.: Condens. Matter 10, 8365 (1998)
W.C. Oliveira, L.N. Oliveira, Phys. Rev. B 49, 11986 (1994)
O. Sakai, Y. Shimizu, T. Kasuya, J. Phys. Soc. Jpn 58, 3666 (1989); W. Izumida, O. Sakai, Y. Shimizu, J. Phys. Soc. Jpn 67, 2444 (1998)
M. Kojima, S. Yotsuhashi, K. Miyake, Acta Phys. Pol. B 22, 1331 (2003); L. De Leo, M. Fabrizio, Phys. Rev. B 69, 245114 (2004)
A.K. Zhuravlev, V.Y. Irkhin, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. Lett. 93, 236403 (2004)
The quarter-filled case is, as far as Hund’s coupling is concerned, of little interest here. However, interesting physics can be found in the presence of a magnetic field (see, for example, Ref. licht_2o)
A.C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, 1993)
R. Bulla, M. Vojta, in Concepts in Electron Correlations, edited by A.C. Hewson, V. Zlatic (Kluwer Academic Publishers, Dordrecht, 2003), p. 209; and references therein
G. Kotliar, H. Kajueter, Phys. Rev. B 54, 14221 (1999)
A. Koga, T. Ohashi, Y. Imai, S. Suga, N. Kawakami, J. Phys. Soc. Jpn 72, 1306 (2003)
J.P. Lu, Phys. Rev. B 49, 5687 (1994)
R. Frésard, G. Kotliar, Phys. Rev. B 56, 12909 (1997); R. Frésard, M. Lamboley, J. Low Temp. Phys. 126, 1091 (2002)
E. Koch, O. Gunnarsson, R.M. Martin, Phys. Rev. B 60, 15714 (1999)
J. Bünemann, W. Weber, Phys. Rev. B 55, 4011 (1997); J. Bünemann, W. Weber, F. Gebhard, Phys. Rev. B 57, 6896 (1998)
A. Koga, N. Kawakami, T.M. Rice, M. Sigrist, Phys. Rev. Lett. 92, 216402 (2004)
A. Liebsch, Phys. Rev. Lett. 91, 226401 (2003)
We have chosen a fixed ration for J/U, because in typical experiments we expect the bandwidth to be the control parameter (through the variation of pressure); this means it is more natural to change U/W and J/W, but keep J/U fixed
Neglect of last term in (2) in fact appears to be non-critical. We therefore concentrate of the spin-flip terms in Hund’s coupling
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Pruschke, T., Bulla, R. Hund’s coupling and the metal-insulator transition in the two-band Hubbard model. Eur. Phys. J. B 44, 217–224 (2005). https://doi.org/10.1140/epjb/e2005-00117-4
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DOI: https://doi.org/10.1140/epjb/e2005-00117-4