An effective Hamiltonian for the two-band Hubbard model was derived by a canonical transformation which was calculated and summed up to infinite order . The transformed Hamiltonian contains terms with strongly renormalized interaction energies. These new interaction energies show sign reversals as a function of the hopping integral in addition to a strong reduction in the charge-transfer gap and a significant increase in the attractive oxygen Hubbard term.
An effective Hamiltonian for the two-band Hubbard model was derived by a canonical transformation which was calculated and summed up to infinite order . The transformed Hamiltonian contains terms with strongly renormalized interaction energies. These new interaction energies show sign reversals as a function of the hopping integral in addition to a strong reduction in the charge-transfer gap and a significant increase in the attractive oxygen Hubbard term.
We compare numerical results of O and Cu occupations and optical and magnetic excitations for the three-band Hubbard model in a Cu4O8 cluster, with those obtained with an effective Hamiltonian Heff in which the Cu-O hopping tpd is eliminated by means of a canonical transformation. This transformation up to order tpd4 is not quantitatively valid when the relevant energy differences are of the order of \ensuremath{\surd}8 tpd or less. However, an Heff with the form of the second-order one, but which retains all higher-order terms contained in a CuO4 (Cu2O7) cluster for zero or one added hole (one added electron) to the undoped system, leads to a very good agreement with the results using the full Hilbert space. This Heff makes possible the numerical study of the three-band Hubbard model for realistic parameters, using larger clusters.
We have studied the Hubbard model with bond-charge interaction on a triangular lattice for a half-filled band. At the point of particle-hole symmetry the model could be analysed in detail in two opposite regimes of the parameter space. Using a real-space renormalization group (RG) we calculate the ground-state energy and the local moment over the whole parameter space. The RG results obey the exact results in the respective limits. In the intermediate region of the parameter space, the RG results clearly show the effects of the non-bipartite geometry of the lattice as well as the absence of symmetry in the reversal of the sign of the hopping matrix element.
We calculate the effective interaction Weff between two holes added to the ground state of the repulsive three-band Hubbard model. To make contact with Cooper theory and with earlier Hubbard model cluster studies, we first use a perturbative canonical transformation, to generate a two-body Hamiltonian. Then, we extend the results to all orders. The approach is exact in principle, and we obtain a close analytic expression including explicitly the effects of all virtual transitions to 4-body intermediate states. Our scheme naturally lends itself to embody off-site, inter-planar, phonon-mediated and other interactions which are not considered in the Hubbard model but may well be important. The result depends qualitatively on the symmetry of the two-hole state: 1B2 and $ ^{1}A_{2}$ pairs are special, because the bare holes do not interact by the on-site repulsion (W=0 pairs). The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid; however Weff is repulsive for Triplet pairs. Bound two-hole states of the same nature were reported earlier in small cluster calculations by exact diagonalisation methods; only symmetric clusters are good models of the plane. Once Weff is known, the pair eigenfunction is determined by an integral equation. We present numerical estimates of the binding energy ∣Δ∣ of the pairs, which is in the physically interesting range of tens of meV if unscreened on-site repulsion parameters are used.
A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transferred from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more ``dressed'' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single-hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to ``undress,'' hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.
We calculate the effective interaction Weff between two holes added to the ground state of the repulsive three-band Hubbard model. To make contact with Cooper theory and with earlier Hubbard model cluster studies, we first use a perturbative canonical transformation, to generate a two-body Hamiltonian. Then, we extend the results to all orders. The approach is exact in principle, and we obtain a close analytic expression including explicitly the effects of all virtual transitions to 4-body intermediate states. Our scheme naturally lends itself to embody off-site, inter-planar, phonon-mediated and other interactions which are not considered in the Hubbard model but may well be important. The result depends qualitatively on the symmetry of the two-hole state: 1 B2 and 1 A2 pairs are special, because the bare holes do not interact by the on-site repulsion (W=0 pairs). The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid; however Weff is repulsive for Triplet pairs. Bound two-hole states of the same nature were reported earlier in small cluster calculations by exact diagonalisation methods; only symmetric clusters are good models of the plane. Once Weff is known, the pair eigenfunction is determined by an integral equation. We present numerical estimates of the binding energy |∆ | of the pairs, which is in the physically interesting range of tens of meV if unscreened on-site repulsion parameters are used. 1 I.
The one-band two-dimensional Hubbard Hamiltonian is analyzed using a real-space renormalization-group block method. The renormalization-group method, previously applied to the one-dimensional case has been extended to two dimensions. It is also shown how to avoid the proliferation of new terms during the process if the shape of the blocks and the symmetries of the kept states are chosen conveniently. We characterize the ground state by its energy per site, the gap of charge excitations, the double occupancy, and the effective hopping. The system shows an insulating behavior in the case of half filling for all nonzero interaction parameter, U, if the hopping is isotropic (ty=tx); that is to say, the gap opens for all positive U, as in the one-dimensional case. If the hopping anisotropy, \ensuremath{\alpha}=ty/tx, is different from the unity and zero the ground state is a conductor up to a critical value (U/t)c1, which depends on \ensuremath{\alpha}. We have analyzed in the same way another filling, n=7/9. The system behaves as a conductor, paramagnetic up to a value (U/t)c2\ensuremath{\sim}2 and weakly ferromagnetic for higher values of U.