Abstract
We calculate the one-particle density of states for the Mott–Hubbard insulating phase of the Hubbard model on a Bethe lattice in the limit of infinite coordination number. We employ the Kato–Takahashi perturbation theory around the strong-coupling limit to derive the Green function. We show that the Green function for the lower Hubbard band can be expressed in terms of polynomials in the bare hole-hopping operator. We check our technique against the exact solution of the Falicov–Kimball model and give explicit results up to and including second order in the inverse Hubbard interaction. Our results provide a stringent test for analytical and numerical investigations of the Mott–Hubbard insulator and the Mott–Hubbard transition within the dynamical mean-field theory. We find that the Hubbard-III approximation is not satisfactory beyond lowest order, but the local-moment approach provides a very good description of the Mott–Hubbard insulator at strong coupling.
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REFERENCES
N.F. Mott, Proc. Phys. Soc. A 62, 416 (1949).
N.F. Mott, Metal—Insulator Transitions, 2nd edition (Taylor and Francis, London, 1990).
F. Gebhard, The Mott Metal—Insulator Transition (Springer, Berlin, 1997).
J. Hubbard, Proc. Roy. Soc. London Ser. A 276, 238 (1963); ibid. 277, 237 (1963).
M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).
J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).
W.F. Brinkman and T.M. Rice, Phys. Rev. B 2, 4302 (1970).
F. Gebhard and A.E. Ruckenstein, Phys. Rev. Lett. 68, 244 (1992); P.-A. Bares and F. Gebhard, Europhys. Lett. 29, 573 (1995).
A. Georges, G. Kotliar, W. Krauth, and M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989).
R.M. Noack and F. Gebhard, Phys. Rev. Lett. 82, 1915 (1999).
J. Schlipf, M. Jarrell, P.G.J. van Dongen, N. Blümer, S. Kehrein, Th. Pruschke, and D. Vollhardt, Phys. Rev. Lett. 82, 4890 (1999).
M.J. Rozenberg, R. Chitra, and G. Kotliar, Phys. Rev. Lett. 83, 3498 (1999).
W. Krauth, Phys. Rev. B 62, 6860 (2000).
R. Bulla, Phys. Rev. Lett. 83, 136 (1999).
R. Bulla, T.A. Costi, and D. Vollhardt, Phys. Rev. B 64, 045103 (2001).
R. Bulla and M. Potthoff, Eur. Phys. J. B 13, 257 (2000); Y. Ono, R. Bulla, A.C. Hewson, and M. Potthoff (unpublished; arXiv cond-mat/0103315).
G. Moeller, Q. Si, G. Kotliar, M.J. Rozenberg, and D.S. Fisher, Phys. Rev. Lett. 74, 2082 (1995).
D.E. Logan and P. Nozières, Phil. Trans. R. Soc. London A 356, 249 (1998); P. Nozières, Eur. Phys. J. B 6, 447 (1998).
S. Kehrein, Phys. Rev. Lett. 81, 3912 (1998).
A. Georges and G. Kotliar, Phys. Rev. Lett. 84, 3500 (2000); S. Kehrein, Phys. Rev. Lett. 84, 3501 (2000).
A. Georges and G. Kotliar, Phys. Rev. B 45, 6479 (1992); X.Y. Zhang, M.J. Rozenberg, and G. Kotliar, Phys. Rev. Lett. 70, 1666 (1993).
Th. Pruschke, D.L. Cox, and M. Jarrell, Europhys. Lett. 21, 593 (1993); Phys. Rev. B 47, 3553 (1993); M. Jarrell, J.K. Freericks, and Th. Pruschke, Phys. Rev. B 51, 11704 (1995).
D.E. Logan, M.P. Eastwood, and M.A. Tusch, Phys. Rev. Lett. 76, 4785 (1996); J. Phys. Cond. Matt. 9, 4211 (1997); M.P. Eastwood, PhD thesis (Oxford University, UK, 1998; unpublished).
M.J. Rozenberg, G. Moeller, and G. Kotliar, Mod. Phys. Lett. B 8, 535 (1994).
M. Caffarel and W. Krauth, Phys. Rev. Lett. 72, 1545 (1994).
L.M. Falicov and J.C. Kimball, Phys. Rev. Lett. 22, 997 (1969).
W. Metzner, P. Schmit, and D. Vollhardt, Phys. Rev. B 45, 2237 (1992); W.F. Brinkman and T.M. Rice, Phys. Rev. B 2, 1324 (1970).
P.G.J. van Dongen and D. Vollhardt, Phys. Rev. Lett. 65, 1663 (1990); P.G.J. van Dongen, Phys. Rev. B 45, 2267 (1992).
E. Economou, Green's Functions in Quantum Physics, 2nd ed. (Springer, Berlin, 1983).
A.L. Fetter and J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
T. Kato, Prog. Theor. Phys. 4, 154 (1949); A. Messiah, Quantum Mechanics, Vol. 2, § 16 (North-Holland, Amsterdam, 1962).
M. Takahashi, J. Phys. C 10, 1289 (1977).
The sign of t in D. Vollhardt, Phys. Rev. Lett. 65, 1663 (1990) Ref. 29 is opposite to our definition which can be cured by another particle-hole transformation.
E.H. Lieb and F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968).
J. Hubbard, Proc. Roy. Soc. London 281, 401 (1964).
D.E. Logan, M.P. Eastwood, and M.A. Tusch, J. Phys. Cond. Matt. 10, 2673 (1998); D.E. Logan and M.T. Glossop, J. Phys. Cond. Matt. 12, 985 (2000); N.L. Dickens and D.E. Logan, Europhys. Lett. 54, 227 (2001); N.L. Dickens and D.E. Logan, J. Phys. Cond. Matt. 13, 4505 (2001).
D. Logan, private communication.
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Kalinowski, E., Gebhard, F. Mott–Hubbard Insulator in Infinite Dimensions. Journal of Low Temperature Physics 126, 979–1007 (2002). https://doi.org/10.1023/A:1013802910383
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DOI: https://doi.org/10.1023/A:1013802910383