Nagaoka ferromagnetism in large-spin systems -Fermion and Boson systems--

TL;DR

This paper investigates magnetic properties of large-spin quantum particles in optical lattices, revealing differences in ferromagnetism conditions between fermionic and bosonic systems, with implications for realizing Nagaoka ferromagnetism.

Contribution

It demonstrates that large-spin fermion systems require stricter lattice conditions for Nagaoka ferromagnetism, while bosonic systems inherently support maximally spin-polarized ground states regardless of lattice details.

Findings

Fermion systems need more stringent lattice connectivity for ferromagnetism.

Bosonic systems with integer spins always have ground states with maximum total spin.

Ground state degeneracy structures differ significantly between fermionic and bosonic large-spin systems.

Abstract

We study magnetic properties of itinerant quantum magnetic particles described by a generalized Hubbard model with large spin ($S>1/2$) which may be realized in optical lattices of laser-cooled atom systems. In fermion systems (half-integer spins), an extended form of Nagaoka ferromagnetism may be realized. However, as novel aspects of the large spin cases, we found that the condition on the lattice connectivity is more stringent than in the case of $S=1/2$ particles, and that the system shows a peculiar degenerate structure of the ground statein which the ferromagnetic state is included. In contrast, it turns out that the ground state of itinerant bosonic systems (integer spins) has a degenerate structure similar to that of fermion system with $S>1/2$ regardless of the shape, connectivity or filling of the lattice, and that the state with the maximum total spin is always one of the ground states.