The Hubbard Model with Local Disorder in d = ∞

  • V. Janiš
  • M. Ulmke
  • D. Vollhardt
Part of the NATO ASI Series book series (NSSB, volume 343)


The scattering of electrons caused by their mutual interaction and by the presence of static disorder, respectively, can lead to very different, and even opposite, effects. For example, on a cubic lattice at half-filling an arbitrarily weak repulsive Hubbard interaction between electrons is sufficient to induce antiferromagnetic long-range order (AFLRO). By contrast, the presence of randomness opposes long-range spatial order. The simultaneous presence of disorder and interactions in electronic systems can hence be expected to lead to fundamentally new phenomena which have no analog in interacting, non-random and non-interacting, disordered systems, respectively [1], To obtain a global picture of the properties of such systems it is desirable to know the solution of a simple, microscopic model which is valid for all input parameters (interaction, disorder, temperature, band filling). Since exact solutions are not available in d = 2, 3 one would like to construct, at least, a thermodynamically consistent mean-field theory that is valid also at strong coupling. Such a (non-perturbative) approximation is provided by the exact solution of a model in d = ∞. It is now known that even in the limit d → ∞ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem [5–8] with infinitely many coupled quantum degrees of freedom. This problem is, in fact, equivalent with an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte-Carlo approach [9]. In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,10] the Mott-Hubbard transition [11–13, 10], transport properties [14] and lately also superconductivity in a two-band version [15] of the Hubbard model in d = ∞.


Hubbard Model Random Potential Antiferromagnetic Phase Magnetic Phase Diagram Band Filling 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • V. Janiš
    • 1
  • M. Ulmke
    • 2
  • D. Vollhardt
    • 1
  1. 1.Institut für Theoretische Physik CTechnische Hochschule AachenAachenGermany
  2. 2.Institut für FestkörperforschungForschungszentrum JülichJülichGermany

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