Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:math-ph/9911010 · Modern Physics Letters A

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

Kazumitsu Sakai, Zengo Tsuboi

Published Nov 20, 1999• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0217732399002522

Related papers

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.

arXiv:math-ph/9912014•International Journal of Modern Physics A•Jun 20, 2000•11 citations

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

Zengo Tsuboi

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.

arXiv:cond-mat/0108358•International Journal of Modern Physics A•Jul 10, 2002•12 citations

Integral equations for thermodynamics of the osp(1|2s) integrable spin chain

Zengo Tsuboi

We propose a system of nonlinear integral equations (NLIE), which gives the free energy of the osp(1|2s) integrable spin chain at finite temperatures. In contrast with usual thermodynamic Bethe ansatz equations, our new NLIE contain only a finite number of unknown functions. On deriving NLIE, we use our osp(1|2s) version of the T-system and the quantum transfer matrix method. Based on our NLIE, we also calculate the high temperature expansion of the free energy and the specific heat.

arXiv:math-ph/0209024•Physics Letters B•Sep 1, 2002•7 citations

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. 1

•Jan 1, 2001•0 citations

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.

arXiv:cond-mat/0011240•Journal of the Physical Society of Japan•Feb 15, 2001•8 citations

Thermodynamics of the Isotropic Heisenberg Quantum Spin Chain

Hans-Peter Eckle

Abstract This chapter presents the extension of the Bethe ansatz to finite temperature, the thermodynamic Bethe ansatz, for the antiferromagnetic isotropic Heisenberg quantum spin chain, the XXX quantum spin chain. It discusses how the added complications of this model arise from the more complicated structure of excitations of the quantum spin chain, the complex string excitations, which have to be included in the Bethe ansatz thermodynamics. It derives the integral equations of the thermodynamic Bethe ansatz for the XXX quantum spin chain and mentions explicit formulas for the free energy of the quantum spin chain and some interesting physical quantities, especially making contact with predictions of conformal symmetry.

•Jul 25, 2019•0 citations
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.
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.
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.
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. 1
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.
Abstract This chapter presents the extension of the Bethe ansatz to finite temperature, the thermodynamic Bethe ansatz, for the antiferromagnetic isotropic Heisenberg quantum spin chain, the XXX quantum spin chain. It discusses how the added complications of this model arise from the more complicated structure of excitations of the quantum spin chain, the complex string excitations, which have to be included in the Bethe ansatz thermodynamics. It derives the integral equations of the thermodynamic Bethe ansatz for the XXX quantum spin chain and mentions explicit formulas for the free energy of the quantum spin chain and some interesting physical quantities, especially making contact with predictions of conformal symmetry.