We present a new way to construct eigenstates of integrable SU(N) spin chains which bypasses the nesting procedure. The states are built by acting on the vacuum with a single operator Bgood(u) evaluated at the Bethe roots. Our proposal serves as a compact alternative to the usual nested Bethe ansatz. Furthermore, the roots of this operator give the separated variables of the model, explicitly generalizing Sklyanin’s approach to the SU(N) case. We also present a similar construction of eigenstates for the SU(1|2) super spin chains.
Based on 1610.08032 and 1805.03927 with N. Gromov and G. Sizov