Bethe state norms for the Heisenberg spin chain in the scaling limit

Abstract

In this paper we discuss the norms of the Bethe states for the spin one-half Heisenberg chain in the critical regime. Our analysis is based on the ODE/IQFT correspondence. Together with numerical work, this has lead us to formulate a set of conjectures concerning the scaling behavior of the norms. Also, we clarify the role of the different Hermitian structures associated with the integrable structure studied in the series of works of Bazhanov, Lukyanov and Zamolodchikov in the mid nineties.

arXiv comment31 pages, 5 figures, v3: minor typos fixed

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• Opers for higher states of the quantum Boussinesq model
• The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
• On the scaling behaviour of an integrable spin chain with ${\mathcal{Z}}_r$ symmetry
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin-$\frac{1}{2}$ chain
• ODE/IQFT correspondence for the generalized affine $\mathfrak{sl}(2)$ Gaudin model