BIMSA > BIMSA Integrable Systems Seminar Anisotropic spin generalization of elliptic Ruijsenaars-Macdonald operators and related integrable long-range spin chains
Anisotropic spin generalization of elliptic Ruijsenaars-Macdonald operators and related integrable long-range spin chains
Organizers
Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Maria Matushko
Time
Friday, May 5, 2023 5:00 PM - 6:30 PM
Venue
Online
Abstract
We propose commuting set of matrix-valued difference operators in terms of the elliptic Baxter-Belavin R-matrix in the fundamental representation of GL(M). In the scalar case M = 1 these operators are the elliptic Ruijsenaars-Macdonald operators, while in the general case they can be viewed as anisotropic versions of the quantum spin Ruijsenaars Hamiltonians. We show that commutativity of the operators for any M is equivalent to a set of R-matrix identities and prove them for the elliptic Baxter-Belavin R-matrix. We show that the Polychronakos freezing trick can be applied to this model. It provides the commuting set of Hamiltonians for long-range spin chain. We also discuss the trigonometric degenerations based on the XXZ R-matrix. The talk is based on joint work with Andrei Zotov arXiv:2201.05944 arXiv:2202.01177