Polynomial Expansion Method for the Monte Carlo Calculation of Strongly Correlated Electron Systems

  • N. Furukawa
  • Y. Motome
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 90)


We present a new Monte Carlo algorithm for a class of strongly correlated electron systems where electrons are strongly coupled to thermodynamically fluctuating classical fields. As an example, the method can be applied to electron- spin coupled systems such as the double-exchange model and dilute magnetic semiconductors, as well as electron-phonon systems. In these systems, calculation of the Boltzmann weights involves quantum-mechanical treatments for the electronic degrees of freedom. The traditional method requires all eigenvalues of the electronic Hamiltonian through a matrix diagonalization. Here we demonstrate that the Boltzmann weight can be obtained by matrix products and trace operations, if the calculation of the density of states is performed through a moment expansion using the Chebyshev polynomials of the Hamiltonian matrix. Therefore, the polynomial expansion method provides a faster calculation for the Boltzmann weights on large-size systems. We also show some results for the application of this algorithm to the study of critical phenomena in the simplified double-exchange model


Monte Carlo Monte Carlo Calculation Polynomial Expansion Hamiltonian Matrix Correlate Electron System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Imada, A. Fujimori, Y. Tokura: Rev. Mod. Phys. 70, 1039 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    N. Furukawa, in Physics of Manganites, Eds. T. Kaplan and S. Mahanti (Plenum Publishing, New York 1999) and references thereinGoogle Scholar
  3. 3.
    Y. Motome and N. Furukawa: J. Phys. Soc. Jpn. 68, 3853 (1999)ADSCrossRefGoogle Scholar
  4. 4.
    L.W. Wang: Phys. Rev. B 49, 10154 (1994)ADSCrossRefGoogle Scholar
  5. 5.
    R.N. Silver and H. Röder: Int. J. Mod. Phys. C 5, 735 (1994)ADSCrossRefGoogle Scholar
  6. 6.
    Y. Motome and N. Furukawa: J. Phys. Soc. Jpn. 70, 1487 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    N. Furukawa and Y. Motome: submitted to J. Phys. Soc. Jpn.Google Scholar
  8. 8.
    C. Zener: Phys. Rev. 82, 403 (1951)ADSCrossRefGoogle Scholar
  9. 9.
    P.W. Anderson and H. Hasegawa: Phys. Rev. 100, 675 (1955)ADSCrossRefGoogle Scholar
  10. 10.
    D.P. Landau and K. Binder: A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge 2000)zbMATHGoogle Scholar
  11. 11.
    Y. Motome and N. Furukawa: J. Phys. Soc. Jpn. 69, 3785 (2000); ibid. 70, 3186 (2001)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • N. Furukawa
    • 1
  • Y. Motome
    • 2
  1. 1.Department of PhysicsAoyama Gakuin UniversitySetagayaJapan
  2. 2.Tokura SSS Project, ERATOJapan Science and Technology CorporationTsukubaJapan

Personalised recommendations