On the emptiness formation probability of the open XXZ spin-$\tf{1}{2}$ chain

TL;DR

This paper analyzes the emptiness formation probability in the open XXZ spin-1/2 chain, deriving explicit formulas and asymptotics at special points and regimes, enhancing understanding of quantum spin chain correlations.

Contribution

It provides a closed form for the emptiness formation probability at a specific anisotropy and boundary condition, and derives asymptotic behaviors across different regimes.

Findings

Closed form for $ au(m)$ at $ riangle=1/2$ with zero boundary field

Leading asymptotics of $ au(m)$ at free fermion point with arbitrary boundary field

Asymptotic behavior of $ au(m)$ in the massless regime $-1< riangle<1$

Abstract

This paper is devoted to the study of the emptiness formation probability $\tau\pa{m}$ of the open XXZ chain. We derive a closed form for $\tau\pa{m}$ at $\Delta=\tf{1}{2}$ when the boundary field vanishes. Moreover we obtain its leading asymptotics for an arbitrary boundary field at the free fermion point. Finally, we compute the first term of the asymptotics of $\ln\pa{\tau\pa{m}}$ in the whole massless regime $-1<\Delta<1$.