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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• Phase transitions in the decomposition of $SU(N)$ representations
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• Exact hole-induced $SU(N)$ flavor-singlets in certain $U=\infty$ $SU(N)$ Hubbard models
• On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet
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• An algebraic approach to revealing magnetic structures of ground states in many-electron systems
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study
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• Optimal Work Extraction from Finite-Time Closed Quantum Dynamics
• Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an SU($N$) Fermi-Hubbard model
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