Communications in Mathematical Physics

, Volume 140, Issue 1, pp 43–62 | Cite as

Absence of highest-spin ground states in the Hubbard model

  • András Sütő
Article

Abstract

The Hubbard modelH=−tΣc c +U Σnxnx withN electrons and periodic boundary condition is studied onv-dimensionalL1 × ... ×L v lattices. It is shown that for any value ofU there is no ground state with maximal spin (S=N/2) in the following cases: (i) ℤ v (v≧2) at low electron densities; with one hole ift>0 andL i is odd for somei; with two holes ift<0, or ift>0 and all theL i are even. (ii) Thebcc lattice at low densities; with two holes ift<0, or ift>0 and all theL i are even; with 2, ..., 6 holes ifL i =L andt<0, or ift>0 andL is even. (iii) The triangular lattice at densities near 0 and 1 ift>0; with two holes ift<0; with 2, 3, 4 holes ift<0 andL1=L2. (iv) Thefcc lattice at densities near 0 and 1 ift>0; with two holes ift<0. Some results for the one dimensional model are also presented.

Keywords

Boundary Condition Neural Network Statistical Physic Complex System Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • András Sütő
    • 1
  1. 1.Institut de Physique ThéoriqueEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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