Nagaoka states in the SU($n$) Hubbard model

Abstract

We present an extension of Nagaoka's theorem in the SU($n$) generalization of the infinite-$U$ Hubbard model. It is shown that, when there is exactly one hole, the fully polarized states analogous to the ferromagnetic states in the SU(2) Hubbard model are ground states. For a restricted class of models satisfying the connectivity condition, these fully polarized states are the unique ground states up to the trivial degeneracy due to the SU($n$) symmetry. We also give examples of lattices in which the connectivity condition can be verified explicitly. The examples include the triangular, kagome, and hypercubic lattices in $d(\ge 2)$ dimensions, among which the cases of $d=2$ and 3 are experimentally realizable in ultracold atomic gases loaded into optical lattices.

9 pages, 7 figures

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Cited by in corpus (3)

• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Analysis and resolution of the ground-state degeneracy of the two-component Bose-Hubbard model
• Upper bound of one-magnon excitation and lower bound of effective mass for ferromagnetic spinor Bose and Fermi gases