HET Journal club: Fedor Levkovich-Maslyuk

Speaker: Fedor Levkovich-Maslyuk

Title: New Construction of Eigenstates and Separation of Variables for SU(N) Spin Chains

Abstract: We conjecture a new way to construct eigenstates of integrable XXX spin chains with SU(N) symmetry. Such spin chains arise in many settings ranging from condensed matter to N=4 SYM. We show that states can be built by repeatedly acting on the vacuum with a single operator Bgood(u) evaluated at the Bethe roots. The proposal serves as a compact alternative to the usual nested algebraic 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 present many tests of the conjecture and prove it in several special cases.
Based on arXiv:1610.08032.