The one-dimensional Hubbard model is characterized by charge-spin separation, but nevertheless in the doped system \ensuremath{\sigma}(\ensuremath{\omega}>0) does not vanish due to a small remaining coupling between charge and spin degrees of freedom. We derive an effective Hamiltonian and give in leading order (\ensuremath{\sim} ${\mathit{J}}^{2}$ ) an analytic expression for \ensuremath{\sigma}(\ensuremath{\omega}) for the case of the Mott insulator doped with one hole. The complete frequency dependence in the strong-coupling limit of the Hubbard model and for the t-J model agrees with results from exact diagonalization. The limit \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) at T=0 is found to be very different for the two models, i.e., \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{3/2}$ in the strong-coupling limit and \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}1/2}$ for the t-J model.The one-dimensional Hubbard model is characterized by charge-spin separation, but nevertheless in the doped system \ensuremath{\sigma}(\ensuremath{\omega}>0) does not vanish due to a small remaining coupling between charge and spin degrees of freedom. We derive an effective Hamiltonian and give in leading order (\ensuremath{\sim}${\mathit{J}}^{2}$) an analytic expression for \ensuremath{\sigma}(\ensuremath{\omega}) for the case of the Mott insulator doped with one hole. The complete frequency dependence in the strong-coupling limit of the Hubbard model and for the t-J model agrees with results from exact diagonalization. The limit \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) at T=0 is found to be very different for the two models, i.e., \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{3/2}$ in the strong-coupling limit and \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}1/2}$ for the t-J model.

Physical review. B, Condensed matterOct 1, 199328 citations

Strong-coupling perturbation theory of the Hubbard model

S. Pairault, David Sénéchal, A.–M. S. Tremblay

arXiv:cond-mat/9905242The European Physical Journal BJun 1, 2000118 citations

Ferromagnetism in multiband Hubbard models: From weak to strong Coulomb repulsion

Karlo Penc, Hiroyuki Shiba, Frédéric Mila +1 more

We propose a mechanism which can lead to ferromagnetism in Hubbard models containing triangles with different on-site energies. It is based on an effective Hamiltonian that we derive in the strong coupling limit. Considering a one-dimensional realization of the model, we show that in the quarter-filled, insulating case the ground state is actually ferromagnetic in a very large parameter range going from Tasaki's flatband limit to the strong coupling limit of the effective Hamiltonian. This result has been obtained using a variety of analytical and numerical techniques. Finally, the same results are shown to apply away from quarter-filling, in the metallic case. \textcopyright{} 1996 The American Physical Society.We propose a mechanism which can lead to ferromagnetism in Hubbard models containing triangles with different on-site energies. It is based on an effective Hamiltonian that we derive in the strong coupling limit. Considering a one-dimensional realization of the model, we show that in the quarter-filled, insulating case the ground state is actually ferromagnetic in a very large parameter range going from Tasaki's flatband limit to the strong coupling limit of the effective Hamiltonian. This result has been obtained using a variety of analytical and numerical techniques. Finally, the same results are shown to apply away from quarter-filling, in the metallic case. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9603042Physical review. B, Condensed matterAug 1, 199670 citations

{\mathit{J}}^{2}

) an analytic expression for \ensuremath{\sigma}(\ensuremath{\omega}) for the case of the Mott insulator doped with one hole. The complete frequency dependence in the strong-coupling limit of the Hubbard model and for the t-J model agrees with results from exact diagonalization. The limit \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) at T=0 is found to be very different for the two models, i.e., \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{3/2}$ in the strong-coupling limit and \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}1/2}$ for the t-J model.