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arXiv:hep-th/9410144 · Modern Physics Letters A

THE QUANTUM ALGEBRAIC STRUCTURE OF THE TWISTED XXZ CHAIN

Mateus Monteiro, I. Roditi, Ligia M. C. S. Rodrigues, S. Sciuto

Published Feb 20, 1995• 8 citations
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Abstract

We consider the quantum inverse scattering method with a new R-matrix depending on two parameters q and t. We find that the underlying algebraic structure is the two-parameter deformed algebra SU q,t(2) enlarged by introducing an element belonging to the center. The corresponding Hamiltonian describes the spin-1/2 XXZ model with twisted periodic boundary conditions.

DOI
10.1142/s0217732395000454

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We consider the quantum inverse scattering method with a new R-matrix depending on two parameters q and t. We find that the underlying algebraic structure is the two-parameter deformed algebra SU q,t(2) enlarged by introducing an element belonging to the center. The corresponding Hamiltonian describes the spin-1/2 XXZ model with twisted periodic boundary conditions.
Exact physical quantities of the D2(2) {D}_2^{(2)} D2(2)​ spin chain model with generic open boundary conditions
A bstract We study the quantum integrable spin chain model associated with the twisted D2(2) {D}_2^{(2)} D2(2)​ D 2 2 algebra (or simply the D2(2) {D}_2^{(2)} D2(2)​ D 2 2 model) under generic open boundary conditions. The Hamiltonian of this model can be factorized into the sum of two staggered XXZ spin chains. Applying the t - W method, we derive the homogeneous Bethe ansatz equations for the zeros of the transfer matrix eigenvalues and the patterns of the corresponding zeros of the staggered XXZ spin chain with generic integrable boundaries. Based on these results, we analytically compute the surface energies and excitation energies of the D2(2) {D}_2^{(2)} D2(2)​ D 2 2 model in different regimes of boundary parameters.
We solve for the spectrum of the deformed biquadratic spin-1 chain by a generalization of the coordinate Bethe ansatz. The model is invariant under the quantum group U q sl(2) and, depending on the deformation parameter q, it's Hamiltonian may not be Hermitian. We consider several boundary conditions and find in particular that for periodic ones, the complete spectrum of the spin- 1/2 XXZ model is always contained in the spectrum of the biquadratic model. For free boundary conditions the spectrum is identical to the XXZ model spectrum, only the multiplicities are, of course, different. Bethe states are highest-weight states of the quantum group, except possibly for zero-energy states.
We construct an open quantum spin chain from the “twisted” [Formula: see text]R matrix in the fundamental representation which has the quantum algebra symmetry Uq[ su (2)]. This anisotropic spin-1 chain is different from the Uq[ su (2)]-invariant chain constructed from the “untwisted” [Formula: see text] spin-1 R matrix (namely, the spin-1 XXZ chain of Fateev-Zamolodchikov with boundary terms) but, nevertheless, is also completely integrable. We discuss the general case of an R matrix of the type g(k), where k∈{1, 2, 3}, and g is any simple Lie algebra.