Ferromagnetism and spin excitations in topological Hubbard models with a flatband

Abstract

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 $\pi$ flux state with topologically nontrivial and nearly-flat electron bands, which can realize either the Chern or $Z_2$ 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 $Z_2$ 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 $Z_2$ 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.

Accepted by PRB

References in corpus (41)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Experimental realisation of the topological Haldane model
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Synthetic magnetic fields for ultracold neutral atoms
• High temperature fractional quantum Hall states
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Fractional quantum Hall effect in the absence of Landau levels
• Superfluidity in topologically nontrivial flat bands
• Fractional Chern Insulator
• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• Ferromagnetism in the Hubbard Model-- Examples from Models with Degenerate Single-Electron Ground States
• Geometric origin of superfluidity in the Lieb lattice flat band
• Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
• Nearly flat band with Chern number C=2 on the dice lattice
• Band geometry, Berry curvature and superfluid weight
• Fractional excitations in the square-lattice quantum antiferromagnet
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Topological flat band models with arbitrary Chern numbers
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• Quantum metric and effective mass of a two-body bound state in a flat band
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Flat bands with higher Chern number in pyrochlore slabs
• Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets
• Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands
• The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models
• Spectral properties of the square-lattice antiferromagnetic J1-J2 Heisenberg model: confinement and deconfinement of spinons
• Topological Hubbard model and its high-temperature quantum Hall effect
• Confinement and Deconfinement of Spinons in Two Dimensions
• Topological Magnons in a One-dimensional Itinerant Flatband Ferromagnet
• Flat-band ferromagnetism in a topological Hubbard model
• Phase diagram and topological phases in the triangular lattice Kitaev-Hubbard model

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