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

Leite, Leonardo S. G.; Doretto, R. L.

doi:10.1103/physrevb.104.155129

Cited by 9 publications

(40 citation statements)

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“…In the present paper, we extend our previous study [32] about the flat-band ferromagnetic phase of a correlated Chern insulator on a honeycomb lattice, by considering a similar, but now time-reversal symmetric, topological Hubbard model on a honeycomb lattice. The noninteracting term of such correlated Z 2 topological insulator is given by a spinfull version of the Haldane model [1] that preserves time-reversal symmetry.…”

Section: Introductionmentioning

confidence: 60%

“…( 36)] excitations. In both cases, we find that the spin-wave excitation spectrum is gapped and constituted by two bands completely separated from each other, a feature that contrasts with the spin-wave spectrum of the correlated Chern insulator [32], whose bands touch at the corners of the first Brillouin zone. Moreover, the spin-wave excitation energies for the mixed-lattice excitations [Fig.…”

Section: Introductionmentioning

confidence: 63%

“…Another set of interacting topological systems that has been recently gaining some attention is made out of lattice models that display (nearly) flat and topologically nontrivial electronic bands in the noninteracting limit [25][26][27][28][29][30][31][32]. In a sense, these papers transport the long discussed subject of flat-band ferromagnetism [33][34][35] to the realm of lattice models with topologically nontrivial freeelectronic bands.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, the merging of these two subjects was motivated by a series of papers [36][37][38] that describe tight-binding models, specially in two dimensions, with only short-range hoppings and whose parameters, once fine tuned, may yield nearly flat and topologically nontrivial electronic bands. In particular, in a previous work [32], we studied the flat-band ferromagnetic phase of a correlated Chern insulator on a honeycomb lattice described by a Haldane-Hubbard model. We considered the model at 1/4 filling (half filling of the lower and doubly degenerated free-electronic band) and in the vicinity of a suitable choice of the model parameters determined in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Similarly to Ref. [32], we consider the topological Hubbard model at 1/4 filling of its noninteracting limit and in the vicinity of the nearly flat band limit [36] of its lower free-electronic band. The flat-band ferromagnetic phase of the time-reversal symmetric topological Hubbard model is described with a bosonization scheme for flat-band correlated Z 2 topological insulators, a formalism that was introduced in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice

Leite¹,

Doretto²

2022

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We study the flat-band ferromagnetic phase of a spinfull and time-reversal symmetric Haldane-Hubbard model on a honeycomb lattice within a bosonization formalism for flat-band Z2 topological insulators. Such a study extend our previous one [L. S. G. Leite and R. L. Doretto, Phys. Rev. B 104, 155129 (2021)] concerning the flat-band ferromagnetic phase of a correlated Chern insulator described by a Haldane-Hubbard model. We consider the topological Hubbard model at 1/4 filling of its corresponding noninteracting limit and in the nearly flat band limit of its lower free-electronic bands. We show that it is possible to define boson operators associated with two distinct spin-flip excitations, one that changes (mixed-lattice excitations) and a second one that preserves (samelattice excitations) the index related with the two triangular sublattices. Within the bosonization scheme, the fermionic model is mapped into an effective interacting boson model, whose quadratic term is considered at the harmonic approximation in order to determine the spin-wave excitation spectrum. For both mixed and same-lattice excitations, we find that the spin-wave spectrum is gapped and has two branches, with an energy gap between the lower and the upper bands at the K and K points of the first Brillouin zone. Such a behavior is distinct from the one of the corresponding correlated Chern insulator, whose spin-wave spectrum has a Goldstone mode at the center of the first Brillouin zone and Dirac points at K and K points. Moreover, we consider the effects on the spin-wave spectrum when an energy offset in the on-site repulsion energies associated with the two triangular sublattices is introduced and when the width of the lower free-electronic bands is increased. We also find some evidences that the spin-wave bands for the same-lattice excitations might be topologically nontrivial even in the completely flat band limit.

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Section: Introductionmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 63%