Itinerant topological magnons in Haldane Hubbard model with a nearly-flat electron band

Gu, Zhao-Long; Dong, Zhao-Yang; Yu, Shun-Li; Li, Jian-Xin

doi:10.48550/arxiv.1908.09255

Cited by 5 publications

(42 citation statements)

References 53 publications

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“…Importantly, it is not clear at the moment whether the finite decay rates found for high-energy spin-wave excitations are an artefact of the bosonization scheme. Even considering these additional approximations, the qualitatively agreement between the real part of the dispersion relation (51) and the numerical spin-wave spectrum [35] indicates that the effective boson model (44) provides an appropriated description for the flat-band ferromagnetic phase of the Haldane-Hubbard model.…”

Section: Summary and Discussionmentioning

confidence: 95%

“…2(a 1 ) from Ref. [35]) while, for a finite ∆U , the energies of the excitations decrease with ∆U and energy gaps open at the K and K points (see Figs. 2(b 1 ) and 2(c 1 ) from Ref.…”

Section: A Effective Interacting Boson Modelmentioning

confidence: 87%

“…( 42)] in order to properly describe the spin-wave excitations at the border of the first Brillouin zone (see Fig. 6) as indicated by the comparison between the dispersion relations (51) and ( 52) and the numerical results [35]. Importantly, it is not clear at the moment whether the finite decay rates found for high-energy spin-wave excitations are an artefact of the bosonization scheme.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…2(b 1 ) and 2(c 1 ) from Ref. [35]). Remarkably, the spin-wave spectrum (51) determined within the bosoniza-tion scheme qualitatively agrees with the numerical one, apart from the fact that the numerical results do not indicate a finite decay rate.…”

Section: A Effective Interacting Boson Modelmentioning

confidence: 98%

“…Gu and collaborators [35] performed exact diagonalization calculations and determined the spin-wave spectrum for the Haldane-Hubbard model (1) in the nearly flat-band limit (18) neglecting the dispersion of the noninteracting electronic bands, which corresponds to the approximation ωαβ q = 0 considered above. For homogeneous on-site Hubbard energies U A = U B , it was found that the spin-wave spectrum has Dirac points at the K and K points (see Fig.…”

Section: A Effective Interacting Boson Modelmentioning

confidence: 99%

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Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model

Leite,

Doretto

2021

Preprint

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We study the flat-band ferromagnetic phase of the Haldane-Hubbard model on a honeycomb lattice within a bosonization scheme for flat-band Chern insulators, focusing on the calculation of the spinwave excitation spectrum. We consider the Haldane-Hubbard model with the noninteracting lower bands in a nearly-flat band limit, previously determined for the spinless model, and at 1/4-filling of its corresponding noninteracting limit. Within the bosonization scheme, the Haldane-Hubbard model is mapped into an effective interacting boson model, whose quadratic term allows us to determine the spin-wave spectrum at the harmonic approximation. We show that the excitation spectrum has two branches with a Goldstone mode and Dirac points at center and at the K and K points of the first Brillouin zone, respectively. We also consider the effects on the spin-wave spectrum due to an energy offset in the on-site Hubbard repulsion energies and due to the presence of an staggered on-site energy term, both quantities associated with the two triangular sublattices. In both cases, we find that an energy gap opens at the K and K points. Moreover, we also find some evidences for an instability of the flat-band ferromagnetic phase in the presence of the staggered on-site energy term. We provide some additional results for the square lattice topological Hubbard model previous studied within the bosonization formalism and comment on the differences between the bosonization scheme implementation for the correlated Chern insulators on both square and honeycomb lattices.

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Section: Summary and Discussionmentioning

confidence: 95%

“…2(a 1 ) from Ref. [35]) while, for a finite ∆U , the energies of the excitations decrease with ∆U and energy gaps open at the K and K points (see Figs. 2(b 1 ) and 2(c 1 ) from Ref.…”

Section: A Effective Interacting Boson Modelmentioning

confidence: 87%

Section: Summary and Discussionmentioning

confidence: 99%

Section: A Effective Interacting Boson Modelmentioning

confidence: 98%

Section: A Effective Interacting Boson Modelmentioning

confidence: 99%

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Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model

Leite,

Doretto

2021

Preprint

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Itinerant Topological Magnons in SU(2) Symmetric Topological Hubbard Models with Nearly Flat Electronic Bands

Gu¹,

Li²

2021

Chinese Phys. Lett.

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We show that a suitable combination of flat-band ferromagnetism, geometry and nontrivial electronic band topology can give rise to itinerant topological magnons. An SU(2) symmetric topological Hubbard model with nearly flat electronic bands, on a Kagome lattice, is considered as the prototype. This model exhibits ferromagnetic order when the lowest electronic band is half-filled. Using the numerical exact diagonalization method with a projection onto this nearly flat band, we can obtain the magnonic spectra. In the flat-band limit, the spectra exhibit distinct dispersions with Dirac points, similar to those of free electrons with isotropic hoppings, or a local spin magnet with pure ferromagnetic Heisenberg exchanges on the same geometry. Significantly, the non-flatness of the electronic band may induce a topological gap at the Dirac points, leading to a magnonic band with a nonzero Chern number. More intriguingly, this magnonic Chern number changes its sign when the topological index of the electronic band is reversed, suggesting that the nontrivial topology of the magnonic band is related to its underlying electronic band. Our work suggests interesting directions for the further exploration of, and searches for, itinerant topological magnons.

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Two-dimensional correlated Chern and topological insulators

da Silva Garcia Leite

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I would like to thank, Prof. Ricardo Luís Doretto, for the orientation, patience and all needed support to the realization of this thesis;Unicamp and IFGW for the welcoming and supporting environment for the students; the university structure that makes my work not only possible but extremely comfortable; all IFGW staff, specially for CPG and DFMC for the excellent support; CNPq for the given opportunity of this Ph.D. scholarship; my wife Ingrid for all her support and inspiration; and to my family and friends, near and distant, who have always supported me in my journey.

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Itinerant topological magnons in Haldane Hubbard model with a nearly-flat electron band

Cited by 5 publications

References 53 publications

Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model

Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model

Itinerant Topological Magnons in SU(2) Symmetric Topological Hubbard Models with Nearly Flat Electronic Bands

Two-dimensional correlated Chern and topological insulators

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