Exact solution of A-D Temperley-Lieb Models

Abstract

We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_q(X_n } for $X_n = A_1,B_n,C_n$and$D_n$. We employ a generalization of the coordinate Bethe-Ansatz developed previously for the deformed biquadratic spin one chain. As expected, all these models have equivalent spectra, i.e. they differ only in the degeneracy of their eigenvalues. This is true for finite length and open boundary conditions. For periodic boundary conditions the spectra of the lower dimensional representations are containded entirely in the higher dimensional ones. The Bethe states are highest weight states of the quantum group, except for some states with energy zero.

References in corpus (1)

• Exact solution of the deformed biquadratic spin 1 hamiltonian

Cited by in corpus (8)

• Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature
• Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
• A Bethe ansatz solution for the closed $U_q[sl(2)]$ Temperley-Lieb quantum spin chains
• Universal Bethe ansatz solution for the Temperley-Lieb spin chain
• On the ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb reflection matrices
• Exact solutions of graded Temperley-Lieb Hamiltonians
• Bethe ansatz for the Temperley-Lieb spin-chain with integrable open boundaries
• Bethe Ansatz solutions for Temperley-Lieb Quantum Spin Chains