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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.

Nordita  | Last modified 02 December 2018 01:17  |  HELP