$T$-system and thermodynamic Bethe ansatz equations for solvable lattice models associated with superalgebras (Bilinear Method in the Study of Integrable Systems and Related Topics)
Year: 2002
Type: article
Abstract: An analytic Bethe ansatz is carried out related to the Lie superal- gebra $osp(1|2s)$ .We present an eigenvahie formula of atransfer matrix in dressed vacuum form (DVF) labeled by aYoung (super) diagram.Remarkable duality among DVFs is found.Acomplete set of transfer matrix functional relations ( $T$ -systern)is proposed as areduction of a Hirota-Miwa equation.We also derive athermodynamic Bethe ansatz (TBA) equation from this $T$ -system and the quantum transfer matrix method.This TBA equation is identical to the one from the string hypothesis.1Introduction Solvable lattice models related to Lie superalgebras [1] $\mathrm{h}_{\dot{\mathrm{e}}}\iota \mathrm{v}(^{\backslash }$ rpceived $\mathrm{I}\mathrm{n}\iota 1(j\mathrm{h}$ attentions [2, 3,4,5,6,7,8,9].To construct cigellval\iota \iota e formulae of transfer matrices for such models is an irnportant problem $\mathrm{i}\mathrm{r}\mathrm{l}$ mathernatical pbysics.To achieve this $\mathrm{p}\mathrm{r}()\mathrm{g}\mathrm{l}\cdot \mathrm{a}\mathrm{l}\mathrm{l}\mathrm{l},$ $\mathrm{t}11(^{\mathrm{Y}}$ Betbe $\dot{\epsilon}\iota \mathrm{r}1_{\iota}\mathrm{s}^{1}\mathrm{a}\mathrm{t}_{l}\mathrm{z}$ has been often $\mathrm{t}1.\mathrm{b}^{\tau}\mathrm{t}^{\backslash}\mathrm{r}1$ .Nowadays, there is nmch $1\mathrm{i}\mathrm{t}\mathrm{I}(^{\mathrm{Y}},1^{\cdot}\dot{c}\mathrm{t}\mathrm{f}\mathrm{u}1^{\cdot}\mathrm{t}^{1}$ (see for $(^{\backslash }\mathrm{X}\dot{\subset}\mathrm{l}_{l}\mathrm{I}\mathrm{r}11^{)}1\mathrm{t}^{1},.'[4.1\mathrm{t}],$$11,12,13$ , 14, 15, 16, 17, 18, 19, $2\mathrm{t}\mathrm{I},$ $21,22,23,\underline{9}4$ ] allcl $\mathrm{r}(^{1\mathrm{f}\backslash }$ ( $\Gamma \mathrm{t}^{\backslash }11\mathrm{C}\mathrm{e}\mathrm{s}$ therein.)$()\mathrm{I}1\mathrm{B}(^{\backslash }\mathrm{t}1_{1\mathrm{t}^{1}}$
Author: Zengo Tsuboi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W109734829