3 research outputs found
Scattering Matrix and Excitation Spectrum of the Hubbard Model
We consider the one-dimensional Hubbard model at half filling. We show that
both excitation spectrum and S-matrix are determined by the SO(4) symmetry of
the model. The complete set of excitations is given by the scattering states
four elementary excitations, which form the fundamental representation of
SO(4). We evaluate the exact S-matrix, which satisfies the Yang-Baxter
relation. The results for the repulsive and attractive Hubbard model are
related by an interchange of spin and charge degrees of freedom.Comment: 8 pages, jyTeX (macro included - just TeX the file) ITP-SB-93-4
A Note on Dressed S-Matrices in Models with Long-Range Interactions
The {\sl dressed} Scattering matrix describing scattering of quasiparticles
in various models with long-range interactions is evaluated by means of
Korepin's method\upref vek1/. For models with -interactions
the S-matrix is found to be a momentum-independent phase, which clearly
demonstrates the ideal gas character of the quasiparticles in such models. We
then determine S-matrices for some models with -interaction
and find them to be in general nontrivial. For the -limit of the
-interaction we recover trivial S-matrices, thus exhibiting
a crossover from interacting to noninteracting quasiparticles. The relation of
the S-matrix to fractional statistics is discussed.Comment: 18 pages, jyTeX (macro included - just TeX the file) BONN-TH-94-13,
revised version: analysis of models with 1/sinh^2 interaction adde
Scaling Limit of the Ising Model in a Field
The dilute A_3 model is a solvable IRF (interaction round a face) model with
three local states and adjacency conditions encoded by the Dynkin diagram of
the Lie algebra A_3. It can be regarded as a solvable version of an Ising model
at the critical temperature in a magnetic field. One therefore expects the
scaling limit to be governed by Zamolodchikov's integrable perturbation of the
c=1/2 conformal field theory. Indeed, a recent thermodynamic Bethe Ansatz
approach succeeded to unveil the corresponding E_8 structure under certain
assumptions on the nature of the Bethe Ansatz solutions. In order to check
these conjectures, we perform a detailed numerical investigation of the
solutions of the Bethe Ansatz equations for the critical and off-critical
model. Scaling functions for the ground-state corrections and for the lowest
spectral gaps are obtained, which give very precise numerical results for the
lowest mass ratios in the massive scaling limit. While these agree perfectly
with the E_8 mass ratios, we observe one state which seems to violate the
assumptions underlying the thermodynamic Bethe Ansatz calculation. We also
analyze the critical spectrum of the dilute A_3 model, which exhibits massive
excitations on top of the massless states of the Ising conformal field theory.Comment: 29 pages, RevTeX, 11 PostScript figures included by epsf, using
amssymb.sty (v2.2