Boundary emptiness formation probabilities in the six-vertex model at $\Delta =-\frac{1}{2}$

Abstract

We define a new family of overlaps $C_{N,m}$ for the XXZ Hamiltonian on a periodic chain of length $N$. These are equal to the linear sums of the groundstate components, in the canonical basis, wherein $m$ consecutive spins are fixed to the state $\uparrow$. We define the boundary emptiness formation probabilities as the ratios $C_{N,m}/C_{N,0}$ of these overlaps. In the associated six-vertex model, they correspond to correlation functions on a semi-infinite cylinder of perimeter $N$. At the combinatorial point $\Delta =-\frac{1}{2}$, we obtain closed-form expressions in terms of simple products of ratios of integers.

51 pages. v2: minor changes

References in corpus (3)

• Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
• On the emptiness formation probability of the open XXZ spin-$\tf{1}{2}$ chain
• Emptiness formation probability and Painlevé V equation in the XY spin chain

Cited by in corpus (5)

• Factorization of density matrices in the critical RSOS models
• Hole probability for noninteracting fermions in a $d$-dimensional trap
• On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta =-1/2$
• Sum rules for the supersymmetric eight-vertex model
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations