Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice
arXiv:2203.15573 · doi:10.1103/PhysRevB.106.155142
Abstract
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 Z topological insulators. Such a study extend our previous one [L. S. G. Leite and R. L. Doretto, Phys. Rev. B {\bf 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 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 (same-lattice 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 and 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 and points. 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.
arXiv comment16 pages, 8 figures, companion paper to our previous arXiv:2106.00468, final version
References in corpus (35)
- Topological Insulators
- Topological insulators and superconductors
- Quantum Spin Hall Effect in Graphene
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Topological Order and the Quantum Spin Hall Effect
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Classification of topological quantum matter with symmetries
- Quantum Spin Hall Effect
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Topological Bands for Ultracold Atoms
- Topological Quantum Matter with Ultracold Gases in Optical Lattices
- From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
- Interacting topological insulators: a review
- Topological quantum matter with cold atoms
- Topological Insulators and Mott Physics from the Hubbard Interaction
- Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
- Correlation effects in two-dimensional topological insulators
- Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model
- Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
- Quantum phase transitions in the Kane-Mele-Hubbard model
- Rashba spin orbit coupling in the Kane-Mele-Hubbard model
- Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands
- Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
- Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
- Z2 topological invariants in two dimensions from quantum Monte Carlo
- Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
- Topological Hubbard model and its high-temperature quantum Hall effect
- Lowest Landau level bosonization
- Ferromagnetism and spin excitations in topological Hubbard models with a flatband
- Topological Magnons in a One-dimensional Itinerant Flatband Ferromagnet
- Flat-band ferromagnetism in a topological Hubbard model
- Analytical approach for the Mott transition in the Kane-Mele-Hubbard model
- Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model