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arXiv:cond-mat/0209423 · Physical Review Letters

Stability of Ferromagnetism in the Hubbard Model on the Kagome Lattice

Akinori Tanaka, Hiromitsu Ueda

Published Feb 14, 2003• 69 citations
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Abstract

The Hubbard model on the kagome lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke [J. Phys. A 24, L73 (1991)]]. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.

DOI
10.1103/physrevlett.90.067204

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The Hubbard model on the kagome lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke [J. Phys. A 24, L73 (1991)]]. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.
The Hubbard model on line graphs has a flat band and highly degenerate ferromagnetic ground states. Here, we study the Hubbard model on a line graph of a planar bipartite graph by adding a special contribution to the kinetic energy which lifts the degeneracy of the lowest single particle state to a general Hamiltonian. We prove that, at half-filling of the lowest band and for sufficiently strong repulsion U , the ground states of this Hamiltonian remain saturated ferromagnetic for a class of line graphs of planar bipartite graphs.
Kagome metals exhibit a rich interplay of topology, electronic correlations, and lattice dynamics. Recent discoveries of Kagome materials with a flat band near the Fermi level have revealed a variety of correlated electronic phases. However, elucidating their microscopic origin remains challenging, as realistic descriptions require accounting for multiple orbitals and competing interactions on an equal footing. To disentangle correlation effects from material-specific details and identify the essential physics of the flat-band regime, we study the single-orbital Kagome-Hubbard model at flat-band fillings using dynamical mean-field theory. We find strong signatures of flat-band ferromagnetism, consistent with exact and mean-field ground-state results. Moreover, we uncover an unconventional quasi-ordered phase in which a partially filled spin-polarized flat band pinned at the Fermi level gives rise to persistent local spin fluctuations down to zero temperature, in striking contrast to the classical behavior expected for a conventional ferromagnet. Our results demonstrate that these anomalous fluctuations are an intrinsic consequence of the flat-band degeneracy and establish a minimal framework for understanding correlation effects in flat-band Kagome systems.
Recently certain Hubbard models with flat lowest bands were proved to exhibit ferromagnetism. Here we study perturbed models with nearly flat bands. We prove that the ferromagnetic state is stable against a single-spin flip for sufficiently large Coulomb interaction UUU, but is unstable for small U>0U>0U>0. This is the first time that the (local) stability of ferromagnetism is proved in nonsingular Hubbard models, in which we must overcome competition between the kinetic energy and the Coulomb interaction.
We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered models do not fall in the class of Mielke-Tasaki flat-band ferromagnets, since they do not obey the connectivity conditions. However, the ground-state ferromagnetism can emerge, if the flat band becomes dispersive. To study this kinetic-energy-driven ferromagnetism we use perturbation theory and exact diagonalization of finite lattices. We find as a typical scenario that small and moderate dispersion may lead to a ferromagnetic ground state for sufficiently large on-site Hubbard repulsion U>UcU>{U}_{c}U>Uc​, where Uc{U}_{c}Uc​ increases monotonically with the acquired bandwidth. However, we also observe for some specific parameter cases, that (i) ferromagnetism appears at already very small Uc{U}_{c}Uc​, (ii) ferromagnetism does not show up at all, (iii) the critical on-site repulsion Uc{U}_{c}Uc​ is a nonmonotonic function of the bandwidth, or that (iv) a critical bandwidth is needed to open the window for ground-state ferromagnetism.
We investigate the magnetization of the ground state of the one-dimensional flat-band Hubbard model as a function of the electron filling, using exact diagonalization techniques. Our calculation shows that the systems with odd n holes added to half-filling bands for a sufficiently large U (the on-site Coulomb repulsion energy) have a saturated ferromagnetic ground state, which is nondegenerate except for the trivial spin degeneracy. Dependences of the critical value of U on the size and on λ (a parameter of the system) are also investigated. For all values of λ, it is found that the ground state is a saturated ferromagnetic state if U is sufficiently large. Moreover, we find that the critical U for the saturated ferromagnetic ground state is almost independent on the system size, at least, for the system near quarter-filling. These facts indicate that even if the system size go to infinity, the ferromagnetic ground state can be exist for a finite U .