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

TL;DR

This paper extends Nagaoka's theorem to the SU(n) Hubbard model, showing that fully polarized states are ground states with one hole, and verifies conditions for specific lattices relevant to ultracold atomic gases.

Contribution

It generalizes Nagaoka's theorem to SU(n) Hubbard models and identifies conditions under which fully polarized states are unique ground states.

Findings

Fully polarized states are ground states with one hole in SU(n) Hubbard model.

Connectivity condition verified for specific lattices like triangular, kagome, and hypercubic.

Applicable to ultracold atomic gases in optical lattices.

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.