### Abstract

A general class of hopping models on a finite bipartite lattice is considered, including the Hubbard model and the Falicov-Kimball model. For the half-filled band, the single-particle density matrix ρ(x,y) in the ground state and in the canonical and grand canonical ensembles is shown to be constant on the diagonal x=y, and to vanish if x=≠=y and if x and y are on the same sublattice. For free electron hopping models, it is shown in addition that there are no correlations between sites of the same sublattice in any higher order density matrix. Physical implications are discussed.

Original language | English (US) |
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Pages (from-to) | 891-898 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 34 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1993 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Lieb, E. H., Loss, M., & McCann, R. J. (1993). Uniform density theorem for the Hubbard model.

*Journal of Mathematical Physics*,*34*(3), 891-898. https://doi.org/10.1063/1.530199