Flat-band ferromagnetism and spin waves in topological Hubbard models

Doretto, R. L.; Goerbig, M. O.

doi:10.1103/physrevb.92.245124

Cited by 17 publications

(103 citation statements)

References 52 publications

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“…Combined with strong Coulomb interactions, nontrivial topological phases can emerge from fractionally filled topological bands. In this article, we are interested in half-filled strongly-correlated nearly-flat topological bands where QAHE can arise 21,37 . The essence for the occurrence of this nontrivial phase is the emergence of itinerant ferromagnetism on nearly-flat bands 28 , which fully polarizes all electron spins.…”

Section: Emergence Of Qahe In Half-filled Nearly-flat Topological mentioning

confidence: 99%

“…The Chern Hubbard model and Z 2 Hubbard model on square lattice described above serve as the paradigm, where half filling of the lower electron band corresponds to quarter filling of the whole system because of the existence of AB sublattices. When t 2 /t 1 takes values in a selected region, the d band and f band are quite flat in that the flatness ratio ∆/W , which is defined as the ratio of the gap ∆ between these two bands to the band-width W of the lower band, can be as large as 4.83 21,37 . In the next subsection, we will introduce the exact diagonalization method with a projection onto the lower nearly-flat electron band to study the spin-1 excitations of the ferromagnetic phases in these two topological Hubbard models.…”

Section: Emergence Of Qahe In Half-filled Nearly-flat Topological mentioning

confidence: 99%

“…Consequently, the charge excitations are gapped and the low energy physics is dominated by the one-spin-flip excitations. These spin-1 excitations have been studied by a generalized bosonization scheme where the interacting fermionic model is mapped to a free bosonic model describing spin-wave excitations at the harmonic approximation 37 . The ferromagnetism was shown to be stable against such spin wave excitations, which are gapless in the Chern Hubbard model and gapped in the Z 2 Hubbard model.…”

Section: Introductionmentioning

confidence: 99%

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Ferromagnetism and spin excitations in topological Hubbard models with a flat band

Dong

et al. 2019

Phys. Rev. B

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We study the spin-1 excitation spectra of the flatband ferromagnetic phases in interacting topological insulators. As a paradigm, we consider a quarter filled square lattice Hubbard model whose free part is the π flux state with topologically nontrivial and nearly-flat electron bands, which can realize either the Chern or Z2 Hubbard model. By using the numerical exact diagonalization method with a projection onto the nearly-flat band, we obtain the ferromagnetic spin-1 excitation spectra for both the Chern and Z2 Hubbard models, consisting of spin waves and Stoner continuum. The spectra exhibit quite distinct dispersions for both cases, in particular the spin wave is gapless for the Chern Hubbard model, while gapped for the Z2 Hubbard model. Remarkably, in both cases, the nonflatness of the free electron bands introduces dips in the lower boundary of the Stoner continuum. It significantly renormalizes the energies of the spin waves around these dips downward and leads to roton-like spin excitations. We elaborate that it is the softening of the roton-like modes that destabilizes the ferromagnetic phase, and determine the parameter region where the ferromagnetic phase is stable. arXiv:1810.11986v2 [cond-mat.str-el]

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Section: Emergence Of Qahe In Half-filled Nearly-flat Topological mentioning

confidence: 99%

Section: Emergence Of Qahe In Half-filled Nearly-flat Topological mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ferromagnetism and spin excitations in topological Hubbard models with a flat band

Dong

et al. 2019

Phys. Rev. B

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“…These arise in a variety of physical settings, such as optical lattices with artificial gauge fields [13][14][15] , layered materials and heterostructures [16][17][18][19] , and itinerant magnets in frustrated lattices [20][21][22] . Within Chern bands, correlated states that either compete or coexist with topological order can emerge with further breaking of symmetries [23][24][25][26][27] . On the other hand, TR-symmetric versions of FCI states may arise in topologically nontrivial bands characterized by a nonzero Z 2 invariant instead of a Chern number 23,28,29 .…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking and the fermionic fractional Chern insulator in topologically trivial bands

Kourtis

2018

Phys. Rev. B

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We describe a mechanism by which fermions in topologically trivial bands can form correlated states exhibiting a fractional quantum Hall (FQH) effect upon introduction of strong repulsive interactions. These states are solid-liquid composites, in which a FQH liquid is induced by the formation of charge order (CO), following a recently proposed paradigm of symmetry-breaking topological (SBT) order [Phys. Rev. Lett. 113, 216404 (2014)]. We devise a spinless fermion model on a triangular lattice, featuring a topologically trivial phase when interactions are omitted. Adding strong short-range repulsion, we first establish a repulsion-driven CO phase at density ρCO = 2/3 particles per site, then dope the model to higher densities ρ = ρCO + ν/6. At ν = 1/3, 2/5 (ρ = 13/18, 11/15), we observe definitive signatures of both CO and the FQH effect -sharply peaked static structure factor, gapped and degenerate energy spectrum and fractionally quantized Hall conductivity σH = 1/3, 2/5 in units of e 2 /h -over a range of all model parameters. We thus obtain direct evidence for fermionic SBT order of FQH type in topologically trivial bands.

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“…Correlation effects in a spinfull topological Hubbard model on a square lattice with nearly-flat noninteracting bands but at a commensurate filling were also discussed [27][28][29]. Here the noninteracting limit of the topological Hubbard model is given by the π-flux model, whose parameters can be adjusted such that the band structure is given by two lower and two higher (doubly degenerated) nearly-flat bands separated by an energy gap [22].…”

Section: Introductionmentioning

confidence: 99%

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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Flat-band ferromagnetism and spin waves in topological Hubbard models

Cited by 17 publications

References 52 publications

Ferromagnetism and spin excitations in topological Hubbard models with a flat band

Ferromagnetism and spin excitations in topological Hubbard models with a flat band

Symmetry breaking and the fermionic fractional Chern insulator in topologically trivial bands

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

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