Solving the n-color ice model
| Autor: | Addona, Patrick, Bockenhauer, Ethan, Brubaker, Ben, Cauthorn, Michael, Conefrey-Shinozaki, Cianan, Donze, David, Dudarov, William, Dukes, Jessamyn, Hardt, Andrew, Li, Cindy, Li, Jigang, Liu, Yanli, Puthanveetil, Neelima, Qudsi, Zain, Simons, Jordan, Sullivan, Joseph, Young, Autumn |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Given an arbitrary choice of two sets of nonzero Boltzmann weights for $n$-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the Yang-Baxter equation. Furthermore we provide an explicit one-dimensional parametrization of all solutions in this case. These $n$-color lattice models are so named because their admissible vertices have adjacent edges labeled by one of $n$ colors with additional restrictions. The two-colored case specializes to the six-vertex model, in which case our results recover the familiar quadric condition of Baxter for solvability. The general $n$-color case includes important solutions to the Yang-Baxter equation like the evaluation modules for the quantum affine Lie algebra $U_q(\hat{\mathfrak{sl}}_n)$. Finally, we demonstrate the invariance of this class of solutions under natural transformations, including those associated with Drinfeld twisting. Comment: 39 pages, 8 figures |
| Databáze: | arXiv |
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