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arXiv · 1409.4099

Quantum spin chains and integrable many-body systems of classical mechanics

A. Zabrodin
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Abstract

This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem for quantum Hamiltonians of the former models is closely related to a sort of inverse spectral problem for Lax matrices of the latter ones. For simplicity, we focus on the most transparent and familiar case of spin chains on N sites constructed by means of the GL(2)-invariant R-matrix. They are related to the classical Ruijsenaars-Schneider system of N particles, which is known to be an integrable deformation of the Calogero-Moser system. As an explicit example the case N=2 is considered in detail.

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A. Zabrodin. 2014-09-14. Quantum spin chains and integrable many-body systems of classical mechanics. https://doi.org/10.1007/978-3-319-14328-6_3

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