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Quantum Spaces pp 161-201 | Cite as

Heisenberg Spin Chains: From Quantum Groups to Neutron Scattering Experiments

  • Jean-Michel Maillet
Part of the Progress in Mathematical Physics book series (PMP, volume 53)

Abstract

Heisenberg spin-1/2 chains are the archetype of quantum integrable one-dimensional models describing magnetic properties of a wide range of compounds (like the KCuF3 crystal), which can be probed experimentally through neutron scattering experiments, while being at the same time at the root of the invention of Bethe ansatz and Yang-Baxter structures that led in turn to quantum groups discovery. The aim of this contribution is to describe these algebraic ingredients and to show how to obtain from them (using combined analytical and numerical analysis) dynamical correlation functions of integrable Heisenberg spin-1/2 chains, the Fourier transform of which, the so-called dynamical structure factors, being directly measured in inelastic neutron scattering experiments. Our method is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem. It leads to recent progress in the computation of integrable Heisenberg spin-1/2 chains correlation functions that we review here.

Keywords

Correlation Function Spin Chain Monodromy Matrix Bethe Equation Heisenberg Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel 2007

Authors and Affiliations

  • Jean-Michel Maillet
    • 1
  1. 1.Laboratoire de PhysiqueENS Lyon et CNRSLyonFrance

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