acta physica slovaca

Acta Physica Slovaca 60, No.2, 155-257 (2010) (104 pages)


Ladislav Ĺ amaj
    1Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia

Full text: ::pdf :: (Received 26 April 2010, accepted 3 May 2010)

Abstract: This is the second part of a three-volume introductory course about integrable systems of interacting bodies. The models of interest are quantum spin chains with nearest-neighbor interactions between spin operators, in particular Heisenberg spin- 2 models. The Ising model in a transverse field, expressible as a quadratic fermion form by using the Jordan-Wigner transformation, is the subject of Sect. 12. The derivation of the coordinate Bethe ansatz for the XXZ Heisenberg chain and the determination of its absolute ground state in various regions of the anisotropy parameter are presented in Sect. 13. The magnetic properties of the ground state are explained in Sect. 14. Sect. 15 concerns excited states and the zero-temperature thermodynamics of the XXZ model. The thermodynamics of the XXZ Heisenberg chain is derived on the basis of the string hypothesis in Sect. 16; the thermodynamic Bethe ansatz equations are analyzed in high-temperature and low-temperature limits. An alternative derivation of the thermodynamics without using strings, leading to a non-linear integral equation determining the free energy, is the subject of Sect. 17. A nontrivial application of the Quantum Inverse Scattering method to the fully anisotropic XYZ Heisenberg chain is described in Section 18. Section 19 deals with integrable cases of isotropic spin chains with an arbitrary spin.

DOI: 10.2478/v10155-010-0002-2

PACS: 02.30.Ik, 05.30.Fk, 05.30.Jp, 05.50.+q, 75.10.Jm
Keywords: Integrable systems, Heisenberg spin chains, Quantum Inverse Scattering method, Yang-Baxter equation, Thermodynamic Bethe ansatz, Magnetic properties
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