MS Seminar (Mathematics - String Theory)

Speaker: Jules Lamers (CEA)
Title: The q-deformed Inozemtsev spin chain
Date (JST): Tue, Jul 25, 2023, 13:30 - 15:00
Place: Seminar Room A
Related File: 3030.pdf
Abstract: The Heisenberg XXX chain admits many deformations that preserve quantum integrability. Some have less spin symmetry, such as the Heisenberg XXZ and XYZ chains. Others have interactions beyond neighbouring spins, allowing one to study the effect of long-range interactions that are inherent in cold atoms and naturally appear in AdS/CFT integrability. The Inozemtsev chain is such a deformation, connecting the Heisenberg XXX chain to the truly long-range Haldane--Shastry chain while remaining exactly solvable throughout. While generally believed to be integrable, there is only a partial proof of commutativity of its conjectured higher hamiltonians, and the underlying algebraic structure is not known.

In this talk I will present a new long-range spin chain that unifies the Inozemtsev and (twisted) Heisenberg XXZ chains. This q-deformed Inozemtsev chain is integrable in that it belongs to a hierarchy of commuting operators. It arises (by 'freezing') from another integrable model with long-range spin interactions that is also new: the elliptic dynamical spin-Ruijsenaars model. Our work presents major progress in the understanding of the integrability of the (isotropic) Inozemtsev chain, and is an important step towards a general theory of long-range integrability.

Based on joint work with Rob Klabbers (arXiv:2306.13066 + in preparation).