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The site-diluted compound (Yb$_{1-x}$Lu$_x$)$_4$As$_3$ is a scarcerealization of the linear Heisenberg antiferromagnet partitioned intofinite-size segments and is an ideal model compound for studyingfield-dependent effects of quenched disorder in the one-dimensionalantiferromagnets. It differentiates from the systems studied so far in twoaspects - the type of randomness and the nature of the energy gap in the puresample. We have measured the specific heat of single-crystal(Yb$_{1-x}$Lu$_x$)$_4$As$_3$ in magnetic fields up to 19.5 T. The contribution$C_{\perp}$ arising from the magnetic subsystem in an applied magnetic fieldperpendicular to the chains is determined. Compared to pure Yb$_4$As$_3$, forwhich $C_{\perp}$ indicates a gap opening, for diluted systems anon-exponential decay is found at low temperatures which is consistent with thethermodynamic scaling of the specific heat established for a Bose-glass phase.

Bose glass behavior in (Yb$_{1-x}$Lu$_x$)$_4$As$_3$ representing the randomly diluted quantum spin-1/2 chains