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Title:
Izergin-Korepin determinant, clustering and Sutherland limit
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Abstract:
The off-shell/on-shell inner product of Bethe states in the XXX model is a partial domain-wall partition function. The latter is represented as a Fredholm determinant with Cauchy-like kernel. The pole part of the integral is evaluated explicitly and the poles organize themselves into arrays (clusters). The integral over the positions of these clusters can be seen as the partition sum of a gas of particles which interact as dipole charges. The Sutherland limit corresponds to the dilute gas approximation in which the pairwise interactions between the particles are neglected.
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