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. arXiv:1906.07636v1 [math-ph]

Exact time evolution formulae in the XXZ spin chain with domain wall initial state

“…Equation (10) looks very similar to exact results which may be found in the literature on the six vertex model with domain wall boundary conditions [37][38][39]. In fact, it is nothing but a limit of one such formula, even though performing this task still requires, as we shall see, a significant amount of work.…”

“…where f (τ ) is given by (A.6). The PDE (38) translates into a PDE for h using (36). Coming back to the original variable z = sin s sin(γ+s) and using the formula for the exact partition function finally yields the result ( 8),( 9) claimed in the introduction.…”

Exact time evolution formulae in the XXZ spin chain with domain wall initial state

“…Equation (10) looks very similar to exact results which may be found in the literature on the six vertex model with domain wall boundary conditions [38][39][40]. In fact, it is nothing but a limit of one such formula, even though performing this task still requires, as we shall see, a significant amount of work.…”