Table of Contents
ISRN Mathematical Physics
Volume 2013, Article ID 410859, 11 pages
Research Article

Eigenstates and Eigenvalues of Chain Hamiltonians Based on Multiparameter Braid Matrices for All Dimensions

1Laboratoire de Physique Théorique, Université d'Oran Es-Sénia, 31100 Oran, Algeria
2Faculté des Sciences et de la Technologie, Centre Universitaire de Aïn Témouchent, 46000 Aïn Témouchent, Algeria
3Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France

Received 4 September 2013; Accepted 14 October 2013

Academic Editors: U. Kulshreshtha and F. Sugino

Copyright © 2013 B. Abdesselam and A. Chakrabarti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study chain Hamiltonians derived from a class of multidimensional, multiparameter braid matrices introduced and explored in a series of previous papers. The N2 × N2 braid matrices (for all N) have free parameters for even N and for N odd. We present systematic explicit constructions for eigenstates and eigenvalues of chain Hamiltonians for and all chain lengths r. We derive explicitly the constraints imposed on these states by periodic (circular) boundary conditions. Our results thus cover both open and closed chains. We then indicate how our formalism can be extended for all . The dependence of the eigenvalues on the free parameters is displayed explicitly, showing how the energy levels and their differences vary in a particular simple way with these parameters. Some perspectives are discussed in conclusion.