Inner products of Bethe states as partial domain wall partition functions

Abstract

We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon state is given by the same expression as the inner product of a 2M-magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular Lx2M grid, with partial domain-wall boundary conditions.

14 pages, 6 figures, typos corrected and a reference added

References in corpus (5)

• A Shortcut to the Q-Operator
• Tailoring Three-Point Functions and Integrability III. Classical Tunneling
• Classical Limit of the Three-Point Function from Integrability
• Partial domain wall partition functions
• XXZ scalar products and KP

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