Exact solutions of graded Temperley-Lieb Hamiltonians

Martin Konôpka, Igor Jex

Lima-Santos, A

Orthosympletic Hamiltonians derived from representations of the Temperley-Lieb algebra are presented and solved via the coordinate Bethe Ansatz. The spectra of these Hamiltonians are obtained using open and closed boundary conditions.

Shao-Ming Fei

We investigate the Temperley–Lieb–Jones algebraic structures in isomorphic higher spin chain models with nearest neighbour interactions and symmetry. The Temperley–Lieb–Jones algebraic constructions for such chains of spins from 1 to are presented. For the case of spin-1 we also give the Temperley–Lieb–Jones algebraic representations related to the anisomorphic spin chain with -deformed symmetry. Their related spin chain Hamiltonians with and symmetries as well as the corresponding solutions of Yang–Baxter equation are also discussed.

Hongzhang Zhuang, Di Zhuang

Carl M. Bender, Gerald V. Dunne

Jan de Gier, Pavel Pyatov

We diagonalize the Hamiltonian of the Temperley–Lieb loop model with open boundaries using a coordinate Bethe ansatz calculation. We find that in the ground-state sector of the loop Hamiltonian, but not in other sectors, a certain constraint on the parameters has to be satisfied. This constraint has a natural interpretation in the Temperley–Lieb algebra with boundary generators. The spectrum of the loop model contains that of the quantum spin-1/2 XXZ chain with non-diagonal boundary conditions. We hence derive a recently conjectured solution of the complete spectrum of this XXZ chain. We furthermore point out a connection with recent results for the two-boundary sine–Gordon model.