Ferromagnetism in d-Dimensional SU(n) Hubbard Models with Nearly Flat Bands

Tamura, Kensuke; Katsura, Hosho

doi:10.1007/s10955-020-02687-w

Cited by 12 publications

(7 citation statements)

References 49 publications

(59 reference statements)

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“…In previous studies, rigorous results regarding the stability of the flat-band ferromagnetism in the SU(2) Hubbard model have been obtained [35,[58][59][60][61][62]. The extension of these results to the SU(N ) case has also been made for a particular class of systems [48,49]. By combining these results with the technique for the proof of Theorem 2, we can also discuss the stability of flat-band ferromagnetism for the ferromagnetic SU(N ) Kondo lattice model in a mathematically rigorous way.…”

Section: Remarkmentioning

confidence: 97%

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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: Remarkmentioning

confidence: 97%

“…Furthermore, extensions of flat-band ferromagnetism to the SU(N ) case have recently been discussed, and rigorous results were proved in Refs. [47][48][49].…”

Section: Introductionmentioning

confidence: 99%

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

Tamura¹,

Katsura²

2023

Preprint

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“…is a fully polarized state. The state (42) corresponds to a ferromagnetic state in SU(N )-symmetric Fermi systems, and therefore we shall call it an SU(N ) ferromagnetic state [52,55,56].…”

Section: Duality Between Primary N -Color η-Pairing States and Su(n )...mentioning

confidence: 99%

“…Even in one dimension, the MHM with more than two components does not admit Bethe-ansatz solutions [47]. While some rigorous results in higher dimensions have been obtained for the two-component case [48][49][50][51], only a few exact results are known for the multicomponent case [52][53][54][55][56][57].…”

Section: Introductionmentioning

confidence: 99%

Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $η$ pairing, weak ergodicity breaking, and partial integrability

Nakagawa¹,

Katsura²,

Ueda³

2022

Preprint

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We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the η-pairing mechanism. Our models include the SU(N ) Hubbard model as a special case. Unlike the conventional two-component case, the generalized η-pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent η pairs. While the η-pairing states in the SU(2) Hubbard model are based on the η-pairing symmetry, the exact eigenstates in the N -component system with N ≥ 3 arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a restricted Hilbert space. We exploit this fact to show that the generalized η-pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the N -component Hubbard models for N ≥ 3. Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a non-interacting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of non-thermalization caused by dissipation. This work establishes the coexistence of off-diagonal longrange order and SU(N ) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators.

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“…[23,25,73,75,77,[79][80][81][82][83][84][85][86][87], electronic systems, see, e.g., Refs. [20][21][22][88][89][90][91][92][93][94][95][96] as well as photonic lattices, see, e.g. Refs.…”

mentioning

confidence: 99%

Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets

Richter,

Ohanyan,

Schulenburg

et al. 2021

Preprint

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The J1-J2 quantum spin sawtooth chain is a paradigmatic one-dimensional frustrated quantum spin system exhibiting unconventional ground-state and finite-temperature properties. In particular, it exhibits a flat energy band of one-magnon excitations accompanied by an enhanced magnetocaloric effect for two singular ratios of the basal interactions J1 and the zigzag interactions J2. In our paper, we demonstrate that one can drive the spin system into a flat-band scenario by applying an appropriate electric field, thus overcoming the restriction of fine-tuned exchange couplings J1 and J2 and allowing one to tune more materials towards flat-band physics, that is to show a macroscopic magnetization jump when crossing the magnetic saturation field, a residual entropy at zero temperature as well as an enhanced magnetocaloric effect. While the magnetic field acts on the spin system via the ordinary Zeeman term, the coupling of an applied electric field with the spins is given by the sophisticated Katsura-Nagaosa-Balatsky (KNB) mechanism, where the electric field effectively acts as a Dzyaloshinskii-Moriya spin-spin interaction. The resulting novel features are corresponding reciprocal effects: We find a magnetization jump driven by the electric field as well as a jump of the electric polarization driven by the magnetic field, i.e. the system exhibits an extraordinarily strong magnetoelectric effect. Moreover, in analogy to the enhanced magnetocaloric effect the system shows an enhanced electrocaloric effect.

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Ferromagnetism in d-Dimensional SU(n) Hubbard Models with Nearly Flat Bands

Cited by 12 publications

References 49 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

Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $η$ pairing, weak ergodicity breaking, and partial integrability

Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets

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