Ferromagnetism in the Hubbard model on a lattice of three coupled chains

Ueda, Hiromitsu; Tanaka, Akinori; Idogaki, Toshihiro

doi:10.1016/j.jmmm.2003.12.1142

Cited by 5 publications

(2 citation statements)

References 6 publications

(8 reference statements)

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“…Other methods of constructing various classes of flat bands have also been proposed [36][37][38][39][40][41]. Based on these methods, various types of flat-band ferromagnetism have been studied so far [42][43][44][45][46]. Furthermore, extensions of flat-band ferromagnetism to the SU(N ) case have recently been discussed, and rigorous results were proved in Refs.…”

Section: Introductionmentioning

confidence: 99%

Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models

Tamura¹,

Katsura²

2023

Preprint

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We develop a general theory of flat-band ferromagnetism in the SU(N ) Fermi-Hubbard model, which describes the behavior of N -component fermions with SU(N ) symmetric interactions. We focus on the case where the single-particle spectrum has a flat band and establish a necessary and sufficient condition for the SU(N ) Hubbard model to exhibit ferromagnetism when the number of particles is the same as the degeneracy. We show that the occurrence of ferromagnetism is equivalent to the irreducibility of the projection matrix onto the space of single-particle ground states. We also demonstrate that this result can be exploited to establish a rigorous result for the ferromagnetic SU(N ) Kondo lattice model with a flat band. Specifically, we prove that when the SU(N ) Hubbard model is ferromagnetic, the ferromagnetic SU(N ) Kondo lattice model with the same hopping matrix also exhibits SU(N ) ferromagnetism.

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Section: Introductionmentioning

confidence: 99%

Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models

Tamura¹,

Katsura²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Other methods of constructing various classes of flat bands have also been proposed [36][37][38][39][40][41]. Based on these methods, various types of flat-band ferromagnetism have been studied so far [42][43][44][45][46]. Furthermore, extensions of flat-band ferromagnetism to the SU(N) case have recently been discussed, and rigorous results were proved in [47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Flat-band ferromagnetism in the SU(N) Hubbard and Kondo lattice models

Tamura,

Katsura

2023

J. Phys. A: Math. Theor.

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We develop a general theory of flat-band ferromagnetism in the SU(N) Fermi-Hubbard model, which describes the behavior of N-component fermions with SU(N) symmetric interactions. We focus on the case where the single-particle spectrum has a flat band at the bottom and establish a necessary and sufficient condition for the SU(N) Hubbard model to exhibit ferromagnetism when the number of particles is the same as the degeneracy. We show that the occurrence of ferromagnetism is equivalent to the irreducibility of the projection matrix onto the space of single-particle ground states. We also demonstrate that this result can be exploited to establish a rigorous result for the ferromagnetic SU(N) Kondo lattice model with a flat band. Specifically, we prove that when the SU(N) Hubbard model is ferromagnetic, the ferromagnetic SU(N) Kondo lattice model with the same hopping matrix also exhibits SU(N) ferromagnetism.

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The Origin of Ferromagnetism

Tasaki

2020

Physics and Mathematics of Quantum Many-Body Systems

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Ferromagnetism in the Hubbard model on a lattice of three coupled chains

Cited by 5 publications

References 6 publications

Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models

Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models

Flat-band ferromagnetism in the SU(N) Hubbard and Kondo lattice models

The Origin of Ferromagnetism

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