The dc conductivity for the t-J model is exactly obtained at t=J and for the Hubbard model in one dimension. Our calculation is carried out for arbitrary band filling by use of the finite-size-scaling method based on the Bethe-ansatz solution under twisted boundary conditions. The effective transport mass defined as the inverse of the conductivity serves as a sensitive probe of the metal-insulator transition. The effective mass is extremely enhanced near half-filling both for the t-J model at t=J and the repulsive Hubbard model, which is a direct evidence of the metal-insulator transition due to the electron correlation. We observe that the large antiferromagnetic coupling J in the t-J model increases the effective mass. On the other hand, the conductivity in the attractive Hubbard model exhibits quite different properties from the repulsive models.
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.
A new integrable model of a strong correlated electronic system is formulated as a model of hole superconductivity. The model is solved by using the Bethe ansatz. The critical exponents describing the decrease of correlation functions on long distances are derived. The behaviour of these correlations indicates that Cooper pairs of holes are formed in the repulsive region of the model. This conclusion is also confirmed by the calculation of the conductivity and the effective transport mass. In the attractive region, the model is a highly conducting system in which the current carriers with small effective mass are 'light fermions'.
The critical exponents for the charge, spin, electron, and superconducting correlation functions of the one-dimensional t-J model at t=J are obtained for arbitrary band filling. Our method is based on the Bethe-ansatz solution and the finite-size scaling analysis in conformal field theory. The long-distance behavior of the model belongs to the same universality class as the repulsive Hubbard model. Near half-filling the exponents take the values expected in the strong-correlation limit of the Hubbard model. In the low-density limit the exponents are those of the noninteracting system.
PACS. 71.10.−w – Theories and models of many electron systems. PACS. 71.10.Fd – Lattice fermion models. PACS. 71.15.Th – Other methods. Abstract. – The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases. Introduction. – New materials whose physics is dominated by electron correlations in narrow energy bands are actually a challenge for solid state physicists. The treatment of such systems is not trivial due to the competition between itinerant and localized behaviour of the electrons in these bands. The Hubbard Hamiltonian [1] is regarded as the simplest model
The three-dimensional repulsive Hubbard model is investigated using the strong-coupling diagram technique. For half-filling, the boundary between paramagnetic and antiferromagnetic states is determined for the range of the Hubbard repulsion
4t≤U≤12t, where
t is the hopping integral between neighboring sites. Along this boundary, the density of states is calculated, and it demonstrates the Mott transition at
U≈9t. For
U≥6t and half-filling, the density of states has the shape inherent in the strong electron repulsion, while for
U=4t, its shape points to weak coupling. The dependence of the Néel temperature
TN on the electron concentration
nˉ is investigated for the cases
U=4t and
12t. In the former case,
TN decreases monotonously with
nˉ, while in the latter case, there is a plateau in the dependence near
nˉ=0.87. The plateau is connected to a reconstruction of the density of states caused by an effective weakening of electron coupling due to electron depopulation. For
U=12t and half-filling, the magnetic critical exponent
γ≈1.4, which is close to the value in the Heisenberg model. Some features resembling the first-order phase transition, revealing themselves in a finite crystal, are discussed.