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Physical Review B

Ferromagnetism in the Hubbard model on a two-leg ladder with interchain Coulomb repulsion

Hiromitsu Ueda, Toshihiro Idogaki

Published Mar 24, 2004• 5 citations
Publisher

Abstract

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 $1/4<n<1/2.$ 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.

DOI
10.1103/physrevb.69.104424

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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 apply perturbation theory and cyclic spin permutation formalism to study the lowest energy states of the infinite-repulsion Hubbard model on n-leg ladders with alternating values of one-site energies αi for neighboring rungs.We establish the "ferromagnetic" character of ladder ground-state at electron densities in the interval 1 -(2n) -1 ≤ ρ ≤ 1 and sufficiently large alternation of one-site energies of neighbor rungs of the ladder.We also show the stability of this state against the small deviations of the values of αi in contrast to the case of two-leg ladder formed by weakly interacting neighbor rungs with equal one-site energies.
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 .
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.
Using the Density Matrix Renormalization Group and two-leg ladders, we investigate an electronic two-orbital Hubbard model including plaquette-diagonal hopping amplitudes. Our goal is to search for regimes where charges added to the undoped state form pairs, presumably a precursor of a superconducting state. For the electronic density $\ensuremath{\rho}=2$, i.e., the undoped limit, our investigations show a robust $(\ensuremath{\pi},0)$ antiferromagnetic ground state, as in previous investigations. Doping away from $\ensuremath{\rho}=2$ and for large values of the Hund coupling JJJ, a ferromagnetic region is found to be stable. Moreover, when the interorbital on-site Hubbard repulsion is smaller than the Hund coupling, i.e., for ${U}^{\ensuremath{'}}<J$ in the standard notation of multiorbital Hubbard models, our results indicate the coexistence of pairing tendencies and ferromagnetism close to $\ensuremath{\rho}=2$. These results are compatible with previous investigations using one-dimensional systems. Although further research is needed to clarify if the range of couplings used here is of relevance for real materials, such as superconducting heavy fermions or pnictides, our theoretical results address a possible mechanism for pairing that may be active in the presence of short-range ferromagnetic fluctuations.
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.
We consider two aspects of the ground state of the $U=\ensuremath{\infty}$ Hubbard ladder: ferromagnetism and the metal-insulator transition at quarter-filling. First, we present rigorous results for the $U=\ensuremath{\infty}$ Hubbard ladder in the limit of the large interchain hopping ${(t}_{\ensuremath{\perp}}/t\ensuremath{\rightarrow}\ensuremath{\infty})$. In this limit, the total spin SSS of the ground state is shown to be zero for the electron density n< 0.5n<~0.5n< 0.5 and its maximum (S=Smax){(S=S}_{\mathrm{max}})(S=Smax​) for n>0.5n>0.5n>0.5. The charge gap at quarter-filling is ${2t}_{\ensuremath{\perp}}.$ We extend these results to finite ${t}_{\ensuremath{\perp}}/t$ by means of the density-matrix renormalization group method. We estimate the phase boundaries with respect to spontaneous magnetization and the charge gap at quarter-filling for finite ${t}_{\ensuremath{\perp}}/t$. Applying the extended Aharonov-Bohm method, we give numerical evidence that the critical ratio ${t}_{\ensuremath{\perp}}/t$, above which the charge gap opens, is less than 0.001. Ferromagnetism in the ttt-JJJ ladder is briefly discussed.