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Journal of Physics A Mathematical and General

Metallic ferromagnetism in the Hubbard model on three coupled chains

Akinori Tanaka, Toshihiro Idogaki

Published Jan 1, 1999• 7 citations
Publisher

Abstract

We study the Hubbard model on three coupled chains which has the saturated ferromagnetic ground states in a finite range of the electron filling factor . In the case that both the single-electron band gap between the highest and lower two bands and the on-site Coulomb interaction are infinitely large, we will rigorously show that the present model exhibits ferromagnetism for 0 < <(1/3), where 0 0 (1/6) depending on the band structure. We will also give numerical results, which indicate that, even in the case that the band gap and the Coulomb interaction are not so large, the present ferromagnetism will survive for suitable electron filling factors.

DOI
10.1088/0305-4470/32/26/307

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We study the Hubbard model on three coupled chains which has the saturated ferromagnetic ground states in a finite range of the electron filling factor . In the case that both the single-electron band gap between the highest and lower two bands and the on-site Coulomb interaction are infinitely large, we will rigorously show that the present model exhibits ferromagnetism for 0 < <(1/3), where 0 0 (1/6) depending on the band structure. We will also give numerical results, which indicate that, even in the case that the band gap and the Coulomb interaction are not so large, the present ferromagnetism will survive for suitable electron filling factors.
We investigate the ground-state magnetic properties of the Hubbard model on a two-leg ladder with interchain Coulomb repulsion. When both the on-site and the interchain Coulomb repulsions are infinitely large, we show exactly that the model exhibits saturated ferromagnetism in the ground states for the electron filling factor 1/4<n<1/2.1/4<n<1/2.1/4<n<1/2. The explicit expression of the saturated ferromagnetic ground state is also obtained. By using numerical calculations, we find that ferromagnetism remains stable for sufficiently large values of these interactions, and that the interchain Coulomb repulsion induces tendencies to ferromagnetism, especially on the 1/4-filling side for small values of the interchain hopping parameter.
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 .
Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrödinger equation has NdN_{\rm d}Nd​-fold degenerate ground states. The degeneracy NdN_{\rm d}Nd​ is proportional to the total number of sites $\absΛ$. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to $ρ_0=N_{\rm d}/(2\absΛ)$, and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.
We present a Hubbard model with a special hopping matrix, which has highly degenerate single-electron energy eigenstates but has different properties than the flat-band Hubbard model. Our model has a paramagnetic ground state when the electron filling factor is less than or equal to quarter-filling. In the case of quarter-filling with one extra electron, the present model exhibits saturated ferromagnetism in the ground states for a sufficiently large value of on-site Coulomb interaction but does not for a small one.
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