1993/03/01 by Élliott H. Lieb, E. H. Lieb, Michael Loss +3 · 33 citations
Mathematics · Physics and Astronomy · #Bipartite graph #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Condensed matter physics #Density matrix #Density of states #Diagonal #Ground state #Hubbard model #Lattice (music) #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Superconductivity #cond-mat
paper · pdf · doi:10.1063/1.530199
published in Journal of Mathematical Physics 34(3), 891-898 (American Institute of Physics) · 15 pages, plaintex, EHLMLRJM-22/Feb/93
openalex publication_date 1993/03/01 · arxiv created 1993/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.