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arXiv:cond-mat/0701207 · Journal of Statistical Mechanics Theory and Experiment

The thermodynamical limit of generalgl(N) spin chains: the vacuum state and densities

Nicolas Crampé, L. Frappat, E. Ragoucy

Published Mar 28, 2007• 4 citations
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Abstract

We study the vacuum state of spin chains where each site carries an arbitrary representation. We prove that the string hypothesis usually used to solve the Bethe ansatz equations is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the centre of the strings for the vacuum. We work through different examples and, in particular, that for spin chains with a periodic array of impurities.

DOI
10.1088/1742-5468/2007/03/p03014

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We study the vacuum state of spin chains where each site carries an arbitrary representation. We prove that the string hypothesis usually used to solve the Bethe ansatz equations is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the centre of the strings for the vacuum. We work through different examples and, in particular, that for spin chains with a periodic array of impurities.
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Using the algebraic Bethe ansatz, we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin ½ Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can be considered in the framework of this approach in the thermodynamic limit. Finally, a multiple integral representation for the spin 1 zero-temperature correlation functions is obtained in the thermodynamic limit.