arXiv:cond-mat/0108358 · International Journal of Modern Physics A

A NOTE ON THE osp(1|2s) THERMODYNAMIC BETHE ANSATZ EQUATION

Zengo Tsuboi

Published Jul 10, 2002• 12 citations

arXiv HTML PDF

Abstract

DOI: 10.1142/s0217751x02009758

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A NOTE ON THE osp(1|2s) THERMODYNAMIC BETHE ANSATZ EQUATION

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THERMODYNAMIC BETHE ANSATZ EQUATION FROM FUSION HIERARCHY OF osp (1|2) INTEGRABLE SPIN CHAIN

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THERMODYNAMIC BETHE ANSATZ EQUATION FOR osp (1|2) INTEGRABLE SPIN CHAIN

Kazumitsu Sakai, Zengo Tsuboi

The thermodynamic Bethe ansatz is applied to a quantum integrable spin chain associated with the Lie superalgebra osp (1|2). Using the string hypothesis, we derive a set of infinite number of nonlinear integral equations (thermodynamic Bethe ansatz equation), which characterize the free energy. The low temperature limit of the free energy is also discussed.

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T-system and thermodynamic Bethe ansatz equations for solvable lattice models associated with superalgebras

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Kazumitsu Sakai, and Zengo Tsuboi

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arXiv:cond-mat/0108358 · International Journal of Modern Physics A

A NOTE ON THE osp(1|2s) THERMODYNAMIC BETHE ANSATZ EQUATION

Zengo Tsuboi

Published Jul 10, 2002• 12 citations

arXiv HTML PDF

Abstract

DOI: 10.1142/s0217751x02009758

Related papers

A NOTE ON THE osp(1|2s) THERMODYNAMIC BETHE ANSATZ EQUATION

A Bethe ansatz equation associated with the Lie superalgebra osp(1|2s) is studied. A thermodynamic Bethe ansatz (TBA) equation is derived by the string hypothesis. The high temperature limit of the entropy density is expressed in terms of the solution of the osp(1|2s) version of the Q-system. In particular for the fundamental representation case, we also derive a TBA equation from the osp(1|2s) version of the T-system and the quantum transfer matrix method. This TBA equation is identical to the one from the string hypothesis. The central charge is expressed by the Rogers dilogarithmic function, and identified to s. 1A Bethe ansatz equation associated with the Lie superalgebra osp(1|2s) is studied. A thermodynamic Bethe ansatz (TBA) equation is derived by the string hypothesis. The high temperature limit of the entropy density is expressed in terms of the solution of the osp(1|2s) version of the Q-system. In particular for the fundamental representation case, we also derive a TBA equation from the osp(1|2s) version of the T-system and the quantum transfer matrix method. This TBA equation is identical to the one from the string hypothesis. The central charge is expressed by the Rogers dilogarithmic function, and identified to s. 1

Jan 1, 20010 citations

THERMODYNAMIC BETHE ANSATZ EQUATION FROM FUSION HIERARCHY OF osp (1|2) INTEGRABLE SPIN CHAIN

KAZUMITSU SAKAI, ZENGO TSUBOI

The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp (1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of the QTM and derive the functional relations among them (T-system) and their certain combinations (Y-system). Their analytical property leads to the nonlinear integral equations which describe the free energy and the correlation length at any finite temperatures. With regard to the free energy, they coincide with the TBA equation based on the string hypothesis.The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp (1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of the QTM and derive the functional relations among them (T-system) and their certain combinations (Y-system). Their analytical property leads to the nonlinear integral equations which describe the free energy and the correlation length at any finite temperatures. With regard to the free energy, they coincide with the TBA equation based on the string hypothesis.

arXiv:math-ph/9912014International Journal of Modern Physics AJun 20, 200011 citations

THERMODYNAMIC BETHE ANSATZ EQUATION FOR osp (1|2) INTEGRABLE SPIN CHAIN

Kazumitsu Sakai, Zengo Tsuboi

arXiv:math-ph/9911010Modern Physics Letters ANov 20, 199911 citations

T-system and thermodynamic Bethe ansatz equations for solvable lattice models associated with superalgebras

Zengo Tsuboi

An analytic Bethe ansatz is carried out related to the Lie superalgebra osp(1|2s). We present an eigenvalue formula of a transfer matrix in dressed vacuum form (DVF) labeled by a Young (super) diagram. Remarkable duality among DVFs is found. A complete set of transfer matrix functional relations (T-system) is proposed as a reduction of a Hirota-Miwa equation. We also derive a thermodynamic 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.An analytic Bethe ansatz is carried out related to the Lie superalgebra osp(1|2s). We present an eigenvalue formula of a transfer matrix in dressed vacuum form (DVF) labeled by a Young (super) diagram. Remarkable duality among DVFs is found. A complete set of transfer matrix functional relations (T-system) is proposed as a reduction of a Hirota-Miwa equation. We also derive a thermodynamic 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.

arXiv:0912.0073Dec 1, 20091 citation

Thermodynamics ofosp(1|2)Integrable Spin Chain: Finite Size Correction

Kazumitsu Sakai, and Zengo Tsuboi

This note is a supplement to our previous papers: Mod. Phys. Lett. A14 (1999) 2427 (math-ph/9911010); Int. J. Mod. Phys. A15 (2000) 2329 (math-ph/9912014). The thermodynamic Bethe ansatz (TBA) equation for an integrable spin chain related to the Lie superalgebra osp(1|2) is analyzed. The central charge determined by low temperature asymptotics of the specific heat can be expressed by the Rogers dilogarithmic function, and identified to be 1. Solving the TBA equation numerically, we evaluate the several thermodynamic quantities. The excited state TBA equation is also discussed.This note is a supplement to our previous papers: Mod. Phys. Lett. A14 (1999) 2427 (math-ph/9911010); Int. J. Mod. Phys. A15 (2000) 2329 (math-ph/9912014). The thermodynamic Bethe ansatz (TBA) equation for an integrable spin chain related to the Lie superalgebra osp(1|2) is analyzed. The central charge determined by low temperature asymptotics of the specific heat can be expressed by the Rogers dilogarithmic function, and identified to be 1. Solving the TBA equation numerically, we evaluate the several thermodynamic quantities. The excited state TBA equation is also discussed.

arXiv:cond-mat/0011240Journal of the Physical Society of JapanFeb 15, 20018 citations

$T$ -system and thermodynamic Bethe ansatz equations for solvable lattice models associated with superalgebras (Bilinear Method in the Study of Integrable Systems and Related Topics)$T$-system and thermodynamic Bethe ansatz equations for solvable lattice models associated with superalgebras (Bilinear Method in the Study of Integrable Systems and Related Topics)

Zengo Tsuboi

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.) $()\mathrm{I}1\mathrm{B}(^{\backslash }\mathrm{t}1_{1\mathrm{t}^{1}}$ 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.)$()\mathrm{I}1\mathrm{B}(^{\backslash }\mathrm{t}1_{1\mathrm{t}^{1}}$

数理解析研究所講究録Aug 1, 20020 citations

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)

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}}