Analytical Bethe Ansatz for quantum-algebra-invariant spin chains

Luca Mezincescu; Rafael I. Nepomechie

doi:10.1016/0550-3213(92)90367-K

Analytical Bethe Ansatz for quantum-algebra-invariant spin chains

Luca Mezincescu, Rafael I. Nepomechie

Physics

Research output: Contribution to journal › Article › peer-review

93 Scopus citations

Abstract

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 U_q[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.

Original language	English (US)
Pages (from-to)	597-621
Number of pages	25
Journal	Nuclear Physics, Section B
Volume	372
Issue number	3
DOIs	https://doi.org/10.1016/0550-3213(92)90367-K
State	Published - Mar 23 1992

ASJC Scopus subject areas

Nuclear and High Energy Physics

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abstract = "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.",

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note = "Funding Information: Center for Physics and at CERN, where part of this work was performed. We also thank M. Monti for his assistance in performing a numerical check on one of our results. This work was supported in part by the National Science Foundation under Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

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N2 - 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.

AB - 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.

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Analytical Bethe Ansatz for quantum-algebra-invariant spin chains

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