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New Construction of Eigenstates and Separation of Variables for SU(N) Spin Chains
(Moscow State University, Physics Department)
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
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
Based on arXiv:1610.08032. with N. Gromov and G. Sizov