Finite Chains with Quantum Affine Symmetries
Abstract
We consider an extension of the (t-U) Hubbard model taking into account new interactions between the numbers of up and down electrons. We confine ourselves to a one-dimensional open chain with L sites (4^L states) and derive the effective Hamiltonian in the strong repulsion (large U) regime. This Hamiltonian acts on 3^L states. We show that the spectrum of the latter Hamiltonian (not the degeneracies) coincides with the spectrum of the anisotropic Heisenberg chain (XXZ model) in the presence of a Z field (2^L states). The wave functions of the 3^L-state system are obtained explicitly from those of the 2^L-state system, and the degeneracies can be understood in terms of irreducible representations of U_q(\hat{sl(2)}).
Cite
@article{arxiv.hep-th/9307103,
title = {Finite Chains with Quantum Affine Symmetries},
author = {F. C. Alcaraz and D. Arnaudon and V. Rittenberg and M. Scheunert},
journal= {arXiv preprint arXiv:hep-th/9307103},
year = {2009}
}
Comments
31pp, Latex, CERN-TH.6935/93. To app. in Int. Jour. Mod. Phys. A. (The title of the paper is changed. This is the ONLY change. Previous title was: Hubbard-Like Models in the Infinite Repulsion Limit and Finite-Dimensional Representations of the Affine Algebra U_q(\hat{sl(2)}). )