Quantum spin chains and integrable many-body systems of classical mechanics
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.
Keywords
Cite
@article{arxiv.1409.4099,
title = {Quantum spin chains and integrable many-body systems of classical mechanics},
author = {A. Zabrodin},
journal= {arXiv preprint arXiv:1409.4099},
year = {2017}
}
Comments
17 pages, misprints corrected, written for Proceedings of the International School and Workshop "Nonlinear Mathematical Physics and Natural Hazards", Sofia, Bulgaria, November 28 - December 2, 2013, to be published in Lecture Notes in Physics