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arXiv · 1810.10996

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

Paul Ryan·Dmytro Volin
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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.

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Paul Ryan, Dmytro Volin. 2020-03-10. Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame. https://doi.org/10.1063/1.5085387

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