Integral formulas and antisymmetrization relations for the six-vertex model

Abstract

We study the relationship between various integral formulas for nonlocal correlation functions of the six-vertex model with domain wall boundary conditions. Specifically, we show how the known representation for the emptiness formation probability can be derived from that for the so-called row configuration probability. A crucial ingredient in the proof is a relation expressing the result of antisymmetrization of some given function with respect to permutations in two sets of its variables in terms of the Izergin-Korepin partition function. This relation generalizes another one obtained by Tracy and Widom in the context of the asymmetric simple exclusion process.

17 pages, no figures

References in corpus (4)

• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction
• Algebraic representation of correlation functions in integrable spin chains
• Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain

Cited by in corpus (3)

• Six-vertex model on a finite lattice: integral representations for nonlocal correlation functions
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Evaluation of integrals for the emptiness formation probability in the square-ice model