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

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 $-1<\Delta<1$.