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We report $\mu$SR measurements on the layered triangular system NaYb$_{1-x}$Lu$_{x}$O$_{2}$ with $x$ = 0.05 and 0.15. We find the quantum disordered ground state [1,2] to be robust and insensitive to magnetic dilution, and exhibiting persistent spin dynamics down to the lowest temperature studied (T = 0.25 K). Indeed, the low temperature muon response is nearly identical to that found for undiluted NaYbO$_{2}$ [2]. We find no evidence for magnetic inhomogeneity, and based on low-temperature longitudinal field studies we propose that our results are best interpreted assuming a magnetically uniform ground state characterized by a cutoff power law spin autocorrelation function.
[1] M. Bordelon et al., Nature Physics $\bf{15}$, 1058 (2019).
[2] L. Ding et al., Phys. Rev. B $\bf{100}$, 144432 (2019).
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