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

The Hubbard model: exact constraints on spectral moments in the strong coupling limit

D. M. Esterling

Exact spectral moment relations are derived and presented for the low temperature, strong coupling limit of the Hubbard model, for any dimension, lattice structure and electron density. These results generate an exact, rigorous and quantitative test for proposed solutions to the Hubbard model that claim to be valid in the strong coupling, low temperature region. The test complements analyses for weak coupling and high temperatures, offering insights into the essential physics of the model, specifically the quasiparticle energy (centroid) and lifetime (width) of the spectral weight function in the infinite coupling, finite hopping limit. Numerical results are given for nearest neighbour hopping in 1, 2 and 3D.Exact spectral moment relations are derived and presented for the low temperature, strong coupling limit of the Hubbard model, for any dimension, lattice structure and electron density. These results generate an exact, rigorous and quantitative test for proposed solutions to the Hubbard model that claim to be valid in the strong coupling, low temperature region. The test complements analyses for weak coupling and high temperatures, offering insights into the essential physics of the model, specifically the quasiparticle energy (centroid) and lifetime (width) of the spectral weight function in the infinite coupling, finite hopping limit. Numerical results are given for nearest neighbour hopping in 1, 2 and 3D.

The Philosophical Magazine A Journal of Theoretical Experimental and Applied PhysicsNov 19, 20220 citations

On the Hubbard model with large coupling

Alain Messager, Сергей Анатольевич Пирогов, Yuri Suhov

Jan 1, 19920 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.