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Integrability of quantum chains: Theory and applications to the spin-1/2 XXZ chain

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Quantum Magnetism

Part of the book series: Lecture Notes in Physics ((LNP,volume 645))

Abstract

In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively we present the treatment of integrable quantum systems at finite temperature on the basis of a lattice path integral formulation and a suitable transfer matrix approach (quantum transfer matrix). The general method, is carried out for the seminal model of the spin-1/2 XXZ chain for which thermodynamic properties like specific heat, magnetic susceptibility and the finite temperature Drude weight of the thermal conductivity are derived.

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Authors and Affiliations

  1. Theoretische Physik, Universität Wuppertal, Gauß-Str. 20, 42097, Wuppertal, Germany

    Andreas Klümper

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  1. Andreas Klümper
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Ulrich Schollwöck Johannes Richter Damian J. J. Farnell Raymod F. Bishop

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© 2004 Springer-Verlag

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Klümper, A. (2004). Integrability of quantum chains: Theory and applications to the spin-1/2 XXZ chain. In: Schollwöck, U., Richter, J., Farnell, D.J.J., Bishop, R.F. (eds) Quantum Magnetism. Lecture Notes in Physics, vol 645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119598

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  • DOI: https://doi.org/10.1007/BFb0119598

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  • Print ISBN: 978-3-540-21422-9

  • Online ISBN: 978-3-540-40066-0

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