Scaling limit of the one-dimensional attractive Hubbard model: The non-half-filled band case

The scaling limit of the less than half filled attractive Hubbard chain is studied. This is a continuum limit in which the particle number per lattice site, n, is kept finite (0<n<1) while adjusting the interaction and bandwidth in a such way that there is a finite mass gap. We construct this limit both for the spectrum and the secular equations describing the excitations. We find, that similarly to the half filled case, the limiting model has a massive and a massless sector. The structure of the massive sector is closely analogous to that of the half filled band and consequently to the chiral invariant SU(2) Gross-Neveu (CGN) model. The structure of the massless sector differs from that of the half filled band case: the excitations are of particle and hole type, however they are not uniquely defined. The energy and the momentum of this sector exhibits a tower structure corresponding to a conformal field theory with c=1 and SU(2)xSU(2) symmetry. The energy-momentum spectrum and the zero temperature free energy of the states with finite density coincides with that of the half filled case supporting the identification of the limiting model with the SU(2) symmetric CGN theory.Comment: Latex, 28 page

Boundary S matrices for the open Hubbard chain with boundary fields

Using the method introduced by Grisaru et al., boundary S matrices for the physical excitations of the open Hubbard chain with boundary fields are studied. In contrast to the open supersymmetric t-J model, the boundary S matrix for the charge excitations depend on the boundary fields though the boundary fields do not break the spin-SU(2) symmetry.Comment: Latex,12 page

Scaling limit of the one-dimensional attractive Hubbard model: The half-filled band case

The scaling limit of the higher level Bethe Ansatz (HLBA) equations for a macroscopically half-filled Hubbard chain is considered. These equations practically decouple into three disjoint sets which are again of the BA type, and correspond to the secular equations of three different kinds of dressed particles (one massive and two massless). The finite size corrections and the fine structure of the spectrum show that the massless sector corresponds to a conformal field with central charge c=1 and Gaussian anomalous dimensions. The zero temperature free energy is also calculated and is found to be in perfect agreement with the results of a perturbative calculation in the SU(2) chiral Gross-Neveu (CGN) model.Comment: LATEX, uses Revtex, 39 page

Exact Drude weight for the one-dimensional Hubbard model at finite temperatures

The Drude weight for the one-dimensional Hubbard model is investigated at finite temperatures by using the Bethe ansatz solution. Evaluating finite-size corrections to the thermodynamic Bethe ansatz equations, we obtain the formula for the Drude weight as the response of the system to an external gauge potential. We perform low-temperature expansions of the Drude weight in the case of half-filling as well as away from half-filling, which clearly distinguish the Mott-insulating state from the metallic state.Comment: 9 pages, RevTex, To appear in J. Phys.

Trapped interacting two-component bosons

In this paper we solve one dimensional trapped SU(2) bosons with repulsive $\delta$-function interaction by means of Bethe-ansatz method. The features of ground state and low-lying excited states are studied by numerical and analytic methods. We show that the ground state is an isospin "ferromagnetic" state which differs from spin-1/2 fermions system. There exist three quasi-particles in the excitation spectra, and both holon-antiholon and holon-isospinon excitations are gapless for large systems. The thermodynamics equilibrium of the system at finite temperature is studied by thermodynamic Bethe ansatz. The thermodynamic quantities, such as specific heat etc. are obtained for the case of strong coupling limit.Comment: 15 pages, 9 figure

Thermodynamics of Kondo Model with Electronic Interactions

On the basis of Bethe ansatz solution of one dimensional Kondo model with electronic interaction, the thermodynamics equilibrium of the system in finite temperature is studied in terms of the strategy of Yang and Yang. The string hypothesis in the spin rapidity is discussed extensively. The thermodynamics quantities, such as specific heat and magnetic susceptibility, are obtained.Comment: 8 pages, 0 figures, Revte

Hubbard physics in the symmetric half-filled periodic Anderson-Hubbard model

Two very different methods -- exact diagonalization on finite chains and a variational method -- are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied $d$ sites as a function of various parameters. In the absence of on-site Coulomb interaction ($U_f$) between $f$ electrons, the two methods yield similar results. The double occupancy of $d$ levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite $U_f$, while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value ($U_d^c$), which depends on $U_f$ and $V$.Comment: 10 pages, 5 figure

A gapless charge mode induced by the boundary states in the half-filled Hubbard open-chain

We discuss the ground state and some excited states of the half-filled Hubbard model defined on an open chain with L sites, where only one of the boundary sites has a different value of chemical potential. We consider the case when the boundary site has a negative chemical potential -p and the Hubbard coupling U is positive. By an analytic method we show that when p is larger than the transfer integral some of the ground-state solutions of the Bethe ansatz equations become complex-valued. It follows that there is a ``surface phase transition'' at some critical value p_c; when p<p_c all the charge excitations have the gap for the half-filled band, while there exists a massless charge mode when p>p_c.Comment: Revtex, 25 pages, 3 eps figures; Full revision with Appendixes adde