TY - GEN

T1 - Quantum spin chains and integrable many-body systems of classical mechanics

AU - Zabrodin, A.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84927743660&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-14328-6_3

DO - 10.1007/978-3-319-14328-6_3

M3 - Conference contribution

AN - SCOPUS:84927743660

T3 - Springer Proceedings in Physics

SP - 29

EP - 48

BT - Nonlinear Mathematical Physics and Natural Hazards - Selected Papers from the International School and Workshop

A2 - Kouteva-Guentcheva, Mihaela

A2 - Aneva, Boyka

A2 - Kouteva-Guentcheva, Mihaela

A2 - Aneva, Boyka

PB - Springer Science and Business Media, LLC

T2 - International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, 2013

Y2 - 28 November 2013 through 2 December 2013

ER -