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International Journal of Modern Physics A

ADDENDUM: INTEGRABILITY OF OPEN SPIN CHAINS WITH QUANTUM ALGEBRA SYMMETRY

Luca Mezincescu, Rafael I. Nepomechie

Published Sep 10, 1992• 70 citations
Publisher

Abstract

In the above reference, we prove that certain quantum spin chains with quantumalgebra symmetry are integrable. Specifically, these are the quantum-algebra-invariant open chains associated with the affine Lie algebras A (1) 1, A(2) 2n, A(2) 2n−1, B(1) n, C (1) n, and D (1)
DOI
10.1142/s0217751x9200257x

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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.
We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz (BA) method. In particular, we determine in this way the spectrum of the transfer matrices of the Uq[su(2)]-invariant spin chains associated with A1(1) and A2(2) in the fundamental representation. The quantum-algebra invariance of these models plays an essential role in obtaining these results. The BA equations for these open chains are “doubled” with respect to the BA equations for the corresponding closed chains.