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arXiv:cond-mat/0204495 · Physica A Statistical Mechanics and its Applications

Generation of new classes of integrable quantum and statistical models

Anjan Kundu

Published Jan 30, 2003• 0 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(02)01419-x

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The aim of this review is to present the list of by now a significant collection of quantum integrable models, ultralocal as well as nonultralocal, in a systematic way stressing on their underlying unifying algebraic structures.We restrict to quantum and statistical models belonging to trigonometric and rational classes with 2 × 2 Lax operators.The ultralocal models can be classified successfully through their associated quantum algebra and are governed by the Yang-Baxter equation, while the nonultralocal models, the theory of which is still in the developmental stage, allow systematization through the braided Yang-Baxter equation.Along with the known integrable models some possible directions for investigation in this field and generation of such new models are suggested.