Theoretical Physics Wednesday Seminar: Paul Ryan

Separated Variables & Wave Functions for rational gl(N) spin chains

We review recent advancements in the Separation of Variables (SoV) program for rational gl(N) spin chains. Building on these, we propose a basis for such spin chains with the physical space in an arbitrary rectangular representation of gl(N) that factorises the Bethe vectors into products of Slater determinants in Baxter Q-functions. This basis is constructed by repeated action of fused transfer matrices on a suitable reference state. We prove that it diagonalises the so-called B-operator, hence the operatorial roots of the latter are the separated variables. The spectrum of the separated variables is also explicitly computed and it turns out to be labelled by Gelfand-Tsetlin patterns, providing a direct link between SoV and Yangian representation theory.