HET- seminar: Volin Dmytro
Speaker: Volin Dmytro
Title: Separated variables and wave functions for rational GL(N) spin chains
Abstract: Integrability of a system can be understood in different ways. One of them is to separate variables thus reducing the system to a collection of “one-dimensional” problems. In this talk we discuss how to separate variables in rational GL(N) XXX spin chains. We discuss how the SV basis is constructed, show that this basis is formed by eigenvectors of the B[good]-operator and that it is naturally labelled by Gelfand-Tsetlin patterns. We also draw analogies with separation of variables in classical (non-quantum) systems described by a spectral curve.
The discussion is valid for spin chains in any rectangular representation and arbitrary rank of the GL(N) symmetry group. For symmetric powers of the defining representation, one also observes a corollary that B[good]-operator acting on a suitably chosen vacuum constructs the eigenstates of the commuting charges.
Based on 1810.10996