392 research outputs found
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
Scaling limit of the one-dimensional XXZ Heisenberg chain with easy axis anisotropy
We construct the scaling limit of the easy axis XXZ chain. This limit is a
subtle combination of approaching the isotropic point, and letting the lattice
spacing to zero to obtain a continuous model with a finite mass gap. We give
the energy difference between the two lowest energy states (the two `vacua')
and analyze the structure of the excitation spectrum of the limiting model. We
find, that the excitations form two sets corresponding to the two vacua. In
both sets the dressed particles are described by Bethe Ansatz like equations
(higher level Bethe Ansatz), and the two sets can be distinguished through a
parameter entering into these secular equations. The degenerations in the
spectrum can be interpreted as originating from an SU(2) symmetry of the
dressed particles. The two particle scattering matrices obtained from the
secular equations are consistent with this symmetry, and they differ in an
overall sign in the two sectors.Comment: 30 pages, RevTe
Physical picture of the gapped excitation spectrum of the one-dimensional Hubbard model
A simple picture for the spectrum of the one-dimensional Hubbard model is
presented using a classification of the eigenstates based on an intuitive
bound-state Bethe-Ansatz approach. This approach allows us to prove a "string
hypothesis" for complex momenta and derive an exact formulation of the
Bethe-Ansatz equations including all states. Among other things we show that
all gapped eigenstates have the Bethe-Ansatz form, contrary to assertions in
the literature. The simplest excitations in the upper Hubbard band are
computed: we find an unusual dispersion close to half-filling.Comment: 22 pages, revtex, 4 eps-figure
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
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
SU(2)xSU(2) Invariant Scattering Matrix of the Hubbard Model
We consider the one-dimensional half-filled Hubbard model. We show that the
excitation spectrum is given by the scattering states of four elementary
excitations, which form the fundamental representation of .
We determine the exact two-particle Scattering matrix, which a solution of the
Yang-Baxter equation and reflects the symmetry of the model. The
results for repulsive and attractive Hubbard model are related by an
interchange of spin and charge degrees of freedom.Comment: 29 pages, jyTeX (macro included - just TeX the file) ITP-SB-93-45,
BONN-HE-93-3
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
-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
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