A representation basis for the quantum integrable spin chain associated with the su(3) algebra

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.

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Exact solution of the sp(4) integrable spin chain with generic boundaries

Journal of High Energy Physics ◽

10.1007/jhep05(2019)067 ◽

2019 ◽

Vol 2019 (5) ◽

Cited By ~ 1

Author(s):

Guang-Liang Li ◽

Junpeng Cao ◽

Panpan Xue ◽

Zhi-Rong Xin ◽

Kun Hao ◽

...

Keyword(s):

Exact Solution ◽

Spin Chain ◽

Integrable Spin

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Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain

Journal of High Energy Physics ◽

10.1007/jhep03(2021)169 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Vladimir V. Bazhanov ◽

Gleb A. Kotousov ◽

Sergei L. Lukyanov

Keyword(s):

Black Hole ◽

Density Matrix ◽

Sigma Models ◽

Spin Chain ◽

Sigma Model ◽

Conformal Symmetry ◽

Scaling Limit ◽

Equilibrium Density ◽

Modular Invariant ◽

Integrable Spin

Abstract This work concerns the quantum Lorentzian and Euclidean black hole non-linear sigma models. For the Euclidean black hole sigma model an equilibrium density matrix is proposed, which reproduces the modular invariant partition function from the 2001 paper of Maldacena, Ooguri and Son. For the Lorentzian black hole sigma model, using its formulation as a gauged SL(2, ℝ) WZW model, we describe the linear and Hermitian structure of its space of states and also propose an expression for the equilibrium density matrix. Our analysis is guided by the results of the study of a certain critical, integrable spin chain. In the scaling limit, the latter exhibits the key features of the Lorentzian black hole sigma model including the same global symmetries, the same algebra of extended conformal symmetry and a continuous spectrum of conformal dimensions.

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

Journal of the Physical Society of Japan ◽

10.1143/jpsj.70.367 ◽

2001 ◽

Vol 70 (2) ◽

pp. 367-371 ◽

Cited By ~ 7

Author(s):

Kazumitsu Sakai ◽

and Zengo Tsuboi

Keyword(s):

Spin Chain ◽

Finite Size ◽

Integrable Spin ◽

Size Correction ◽

Finite Size Correction

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Integrable spin chain with reflecting end

Journal of Physics A General Physics ◽

10.1088/0305-4470/29/14/021 ◽

1996 ◽

Vol 29 (14) ◽

pp. 3977-3984 ◽

Cited By ~ 30

Author(s):

Takashi Yamamoto ◽

Osamu Tsuchiya

Keyword(s):

Spin Chain ◽

Integrable Spin

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

Modern Physics Letters A ◽

10.1142/s0217732399002522 ◽

1999 ◽

Vol 14 (35) ◽

pp. 2427-2435 ◽

Cited By ~ 9

Author(s):

KAZUMITSU SAKAI ◽

ZENGO TSUBOI

Keyword(s):

Free Energy ◽

Low Temperature ◽

Bethe Ansatz ◽

Infinite Number ◽

Spin Chain ◽

Lie Superalgebra ◽

Temperature Limit ◽

Nonlinear Integral Equations ◽

Thermodynamic Bethe Ansatz ◽

Integrable Spin

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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