Universal Bethe ansatz solution for the Temperley-Lieb spin chain

Understand

We consider the Temperley-Lieb (TL) open quantum spin chain with "free" boundary conditions associated with the spin-$s$ representation of quantum-deformed $sl(2)$.

• We construct the transfer matrix, and determine its eigenvalues and the corresponding Bethe equations using analytical Bethe ansatz.
• We show that the transfer matrix has quantum group symmetry, and we propose explicit formulas for the number of solutions of the Bethe equations and the degeneracies of the transfer-matrix eigenvalues.
• We propose an algebraic Bethe ansatz construction of the off-shell Bethe states, and we conjecture that the on-shell Bethe states are highest-weight states of the quantum group.