Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame

TL;DR

This paper introduces a new basis for rational gl(N) spin chains that simplifies the diagonalization process by factorizing Bethe vectors into determinants, explicitly computing the spectrum of separated variables.

Contribution

It constructs a basis that factorizes Bethe vectors into determinants and explicitly computes the spectrum of separated variables for rational gl(N) spin chains.

Findings

Basis factorizes Bethe vectors into Slater determinants.

Spectrum of separated variables labeled by Gelfand-Tsetlin patterns.

Simplified derivations using a special twist choice.

Abstract

We propose a basis for rational gl(N) spin chains in an arbitrary rectangular representation $(S^A)$ 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. Our approach utilises a special choice of the spin chain twist which substantially simplifies derivations.