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

OKC/Nordita High-Energy Physics Theory seminar

Tuesday 04 December 2018
from 10:45
to 11:45 at
132:028

Speaker :

Paul Ryan (University of Dublin)

Abstract :

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.