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 2 M -magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular L × 2 M grid, with partial domain-wall boundary conditions.
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ArXiv ePrint: 1207.2562
Associate member of the Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussée, 1784 Sofia, Bulgaria. (Ivan Kostov)
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Kostov, I., Matsuo, Y. Inner products of Bethe states as partial domain wall partition functions. J. High Energ. Phys. 2012, 168 (2012). https://doi.org/10.1007/JHEP10(2012)168
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DOI: https://doi.org/10.1007/JHEP10(2012)168