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New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
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We conjecture a new way to construct eigenstates of integrable XXX quantum spin chains with SU(N) symmetry. The states are built by repeatedly 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 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. We focus on rational spin chains with fundamental representation at each site, but expect many of the results to be valid more generally.
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Bethe Ansatz without Nesting
Non-nested Bethe equations for gl_ℓ vector spin chains encode the full spectrum in the roots of Q1(u) alone via a hierarchy of transfer-matrix regularity conditions closing at R_ℓ=0.
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