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

2000 ◽  
Vol 15 (15) ◽  
pp. 2329-2346 ◽  
Author(s):  
KAZUMITSU SAKAI ◽  
ZENGO TSUBOI
Keyword(s):  
Free Energy ◽  
Excited State ◽  
Bethe Ansatz ◽  
Spin Chain ◽  
Lie Superalgebra ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Functional Relations ◽  
Integrable Spin ◽  
T System

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.

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

1999 ◽  
Vol 14 (35) ◽  
pp. 2427-2435 ◽  
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.

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

2002 ◽  
Vol 17 (17) ◽  
pp. 2351-2368 ◽  
Author(s):  
ZENGO TSUBOI
Keyword(s):  
Bethe Ansatz ◽  
Central Charge ◽  
Lie Superalgebra ◽  
Temperature Limit ◽  
Entropy Density ◽  
Fundamental Representation ◽  
Thermodynamic Bethe Ansatz ◽  
High Temperature Limit ◽  
The One ◽  
T System

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.

Thermodynamics of the Isotropic Heisenberg Quantum Spin Chain

2019 ◽  
pp. 641-654
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Free Energy ◽  
Bethe Ansatz ◽  
Finite Temperature ◽  
Spin Chain ◽  
Conformal Symmetry ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Explicit Formulas ◽  
Thermodynamic Bethe Ansatz ◽  
Physical Quantities

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.

The Thermodynamic Bethe Ansatz and a Connection with Painlevé Equations

1997 ◽  
Vol 11 (01n02) ◽  
pp. 69-74
Author(s):  
Craig A. Tracy ◽  
Harold Widom
Keyword(s):  
Integral Equations ◽  
Bethe Ansatz ◽  
Painlevé Equations ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Painleve Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We summarize some recent connections between a class of nonlinear integral equations related to the thermodynamic Bethe Ansatz and a class of linear integral equations related to the Painlevé equations.

NLIE METHOD FOR THE SPECTRAL PROBLEM OF AdS5 × S5

2013 ◽  
Vol 21 ◽  
pp. 165-166
Author(s):  
RYO SUZUKI
Keyword(s):  
Excited State ◽  
Spectral Problem ◽  
Integral Equations ◽  
Integrable Systems ◽  
Degrees Of Freedom ◽  
Condensed Matter ◽  
Nonlinear Integral Equations ◽  
Dynamical Degrees ◽  
T System

The excited state spectrum of AdS5 × S5 string can be computed exactly by the mirror TBA equations. We discuss an equivalent, smaller set of equations called hybrid nonlinear integral equations (NLIE). The hybrid NLIE is written by new dynamical degrees of freedom, analogous to spinon variables in condensed matter systems. This derivation is applicable to any integrable systems which obey A1 T-system equipped with certain analyticity conditions. A case study of orbifold Konishi state shows that the new method relieves the problem of criticality in the mirror TBA equations.

scholarly journals Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Large Class ◽  
Bethe Ansatz ◽  
Difference Equations ◽  
The Other ◽  
Elementary Functions ◽  
Quantum Dilogarithm ◽  
Thermodynamic Bethe Ansatz ◽  
Dilogarithm Function ◽  
Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

scholarly journals Encoding Information on the Excited State of a Molecular Spin Chain

2021 ◽  
pp. 2009467
Author(s):  
Kostantine Katcko ◽  
Etienne Urbain ◽  
Franck Ngassam ◽  
Lalit Kandpal ◽  
Bhavishya Chowrira ◽  
...  
Keyword(s):  
Excited State ◽  
Spin Chain ◽  
Molecular Spin

scholarly journals T − W relation and free energy of the Heisenberg chain at a finite temperature

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Pengcheng Lu ◽  
Yi Qiao ◽  
Junpeng Cao ◽  
Wen-Li Yang ◽  
Kang jie Shi ◽  
...  
Keyword(s):  
Free Energy ◽  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Chain ◽  
Quantum Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Lattice Quantum ◽  
Quantum Integrable Models ◽  
Invariant Quantum

Abstract A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

Sign in / Sign up

Export Citation Format

Share Document