  Topological properties of physical systems are attracting tremendous
interest. Recently, magnetic solid state compounds with and without magnetic
order have become a focus. We show that ${\text{BiCu}}_{2}{\text{PO}}_{6}$ is
the first gapful quantum antiferromagnet with a finite Zak phase, which
characterises one-dimensional systems, and only the second with topological
non-trivial triplon excitations. Surprisingly, in spite of the bulk-boundary
correspondence no localised edge mode occurs. This unexpected behaviour is
explained by the distinction between direct and indirect gaps among the triplon
bands.
