J. M. P. Carmelo, P. D. Sacramento
This paper presents the second part of a study on the elementary objects of the 1D Hubbard model that emerge from the interplay of its global symmetry with the exact Bethe-ansatz (BA) solution. Here we introduce and study the corresponding scattering theory and its scatterers and scattering centers that naturally emerge from the present formulation elementary objects. The theory refers to the excited states of ground states with arbitrary values of the densities and finite repulsive interaction. The unbound spinons and unbound $\eta$-spinons whose occupancies generate the energy eigenstates outside the BA solution subspace are found to be neither scatterers nor scattering centers. Those are rather the $c$ pseudofermions and composite spin-neutral $2\nu$-spinon pseudofermions and $\eta$-spin-neutral $2\nu$-$\eta$-spinon pseudofermions. Here $\nu=1,2,...$ is the number of spinon or $\eta$-spinon pairs. Each ground-state - excited-state transition is associated with a well defined set of elementary zero-momentum forward-scattering events. The pseudofermion scatterers dressed $S$ matrix is expressed as a commutative product of $S$ matrices, each corresponding to an elementary two-pseudofermion scattering event.The momentum dependence of the exponents characterizing the high-energy correlation function singularities of the metallic phases of a wide class of 1D integrable and non-integrable systems is in the present exactly solvable model found to be fully controlled by the phase shifts and corresponding dressed $S$ matrix introduced in this paper. The relation of the elementary objects considered here and in the first paper to the traditional holon and spinon descriptions is clarified.
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http://arxiv.org/abs/1211.6073
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