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arXiv:cond-mat/9801242 · Physical review. B, Condensed matter

Flat-band ferromagnetism induced by off-site repulsions

Ryotaro Arita, Yukihiro Shimoi, Kazuhiko Kuroki, Hideo Aoki

Published May 1, 1998• 15 citations
arXivHTMLPDF

Abstract

The density-matrix renormalization-group method is used to analyze how the nearest-neighbor repulsion $V$ added to the Hubbard model on a one-dimensional triangular lattice and a railway-trestle ${(t\ensuremath{-}t}^{\ensuremath{'}})$ model will affect the electron-correlation-dominated ferromagnetism arising from the interference (frustration). The obtained phase diagram shows that there is a region in the small-${t}^{\ensuremath{'}}$ side where the critical on-site repulsion above which the system becomes ferromagnetic is reduced when the off-site repulsion is introduced.

DOI
10.1103/physrevb.57.10609

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The density-matrix renormalization-group method is used to analyze how the nearest-neighbor repulsion VVV added to the Hubbard model on a one-dimensional triangular lattice and a railway-trestle (t\ensuremath−t\ensuremath′){(t\ensuremath{-}t}^{\ensuremath{'}})(t\ensuremath−t\ensuremath′) model will affect the electron-correlation-dominated ferromagnetism arising from the interference (frustration). The obtained phase diagram shows that there is a region in the small-t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ side where the critical on-site repulsion above which the system becomes ferromagnetic is reduced when the off-site repulsion is introduced.
We examined a one-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping with up to 32 sites by means of the density-matrix renormalization-group method. The model has two energy bands and includes the flat-band model studied by Tasaki as a special case. The model with finite band dispersion is found to show metallic (saturated) ferromagnetism for a sufficiently strong interaction. No partially polarized ground state is found. The interaction necessary to realize a ferromagnetic ground state becomes weak when the electron density is decreased from the quarter-filling.
The authors investigated the frustration effect when next-nearest-electron hopping causes itinerant ferromagnetism in a one-dimensional Hubbard model.By using the exact diagonalization method and the density-matrix renormalization-group technique,it was shown that the next-nearest electron hopping term stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n when the system is small.Furthermore,by calculating the local spin-spin correlation function,we found the ferromagnetic state becomes unstable as the length of the system increases.A further study showed that the ferromagnetic relationships of the system become weaker when the system's size increases.In addition,the system will transit to the anti-ferromagnetic correlation when the system reaches critical length.These observed results demonstrate on the one hand that an itinerant ferromagnetic phase exists in the electron-mixing area of small-sized material in the one-dimensional Hubbard model,and on the other hand,these observations should be helpful in understanding the origin of the itinerant ferromagnetism observed recently in some metallic and metallic oxide clusters.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
Phase diagram of the Hubbard-Holstein model in the coexistence of electron-electron and electron-phonon interactions has been theoretically obtained with the density-matrix renormalization group method for one-dimensional systems, where an improved warm-up (the recursive sweep) procedure has enabled us to calculate various correlation functions. We have examined the cases of (i) the systems half-filled by electrons for the full parameter space spanned by the electron-electron and electron-phonon coupling constants and the phonon frequency, (ii) non-half-filled system, and (iii) trestle lattice. For (i), we have detected a region where both the charge and on-site pairing correlations decay with power laws in real space, which suggests a metallic behavior. While pairing correlations are not dominant in (i), we have found that they become dominant as the system is doped in (ii) or as the electronic band structure is modified (with a broken electron-hole symmetry) in (iii) in certain parameter regions.
We present rigorous results for the SU(n)\mathrm{SU}(n)SU(n) Fermi-Hubbard model on the railroad-trestle lattice. We first study the model with a flat band at the bottom of the single-particle spectrum and prove that the ground states exhibit SU(n)\mathrm{SU}(n)SU(n) ferromagnetism when the total fermion number is the same as the number of unit cells. We then perturb the model by adding extra hopping terms and make the flat band dispersive. Under the same filling condition, it is proved that the ground states of the perturbed model remain SU(n)\mathrm{SU}(n)SU(n) ferromagnetic when the bottom band is nearly flat. This is the first rigorous example of the ferromagnetism in nonsingular SU(n)\mathrm{SU}(n)SU(n) Hubbard models in which both the single-particle density of states and the on-site repulsive interaction are finite.
The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.