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Birkhäuser Boston eBooks

Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain

Jean Michel Maillet

Published Jan 1, 2002• 0 citations
Publisher

Abstract

A general approach to the computation of exact correlation functions of lattice quantum integrable models proposed recently is reviewed. It is based on the resolution of the quantum inverse scattering problem. The application of this method to theXXZ Heisenberg spin- $$\tfrac{1}{2}$$ in a magnetic field leads to multiple integral representations of its n-point correlation functions. For zero magnetic field, it gives a proof, in both the massless and massive (anti-ferromagnetic) regimes, of the formulas obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra $${\mathcal{U}_q}(\widehat s{l_2})$$ together with the corner transfer matrix approach (massive regime). We also discuss further problems, related in particular to long distance asymptotics of these correlation functions.

DOI
10.1007/978-1-4612-0087-1_12

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