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Topological properties of physical systems are attracting tremendousinterest. Recently, magnetic solid state compounds with and without magneticorder have become a focus. We show that ${\text{BiCu}}_{2}{\text{PO}}_{6}$ isthe first gapful quantum antiferromagnet with a finite Zak phase, whichcharacterises one-dimensional systems, and only the second with topologicalnon-trivial triplon excitations. Surprisingly, in spite of the bulk-boundarycorrespondence no localised edge mode occurs. This unexpected behaviour isexplained by the distinction between direct and indirect gaps among the triplonbands.

Non-trivial topology of the quasi-one-dimensional triplons in the quantum antiferromagnet ${\text{BiCu}}_{2}{\text{PO}}_{6}$