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The two-point clustering of dark matter halos is influenced by haloproperties besides mass, a phenomenon referred to as halo assembly bias. Usingthe depth of the gravitational potential well, $V_{\rm max}$, as our secondaryhalo property, in this paper we present the first study of the scale-dependenceassembly bias. In the large-scale linear regime, $r\geq10h^{-1}{\rm Mpc},$ ourfindings are in keeping with previous results. In particular, at the low-massend ($M_{\rm vir}<M_{\rm coll}\approx10^{12.5}{\rm M}_{\odot}$), halos withhigh-$V_{\rm max}$ show stronger large-scale clustering relative to halos withlow-$V_{\rm max}$ of the same mass, this trend weakens and reverses for $M_{\rmvir}\geq M_{\rm coll}.$ In the nonlinear regime, assembly bias in low-masshalos exhibits a pronounced scale-dependent "bump" at $500h^{-1}{\rmkpc}-5h^{-1}{\rm Mpc},$ a new result. This feature weakens and eventuallyvanishes for halos of higher mass. We show that this scale-dependent signaturecan primarily be attributed to a special subpopulation of ejected halos,defined as present-day host halos that were previously members of a higher-masshalo at some point in their past history. A corollary of our results is thatgalaxy clustering on scales of $r\sim1-2h^{-1}{\rm Mpc}$ can be impacted by upto $\sim15\%$ by the choice of the halo property used in the halo model, evenfor stellar mass-limited samples.

The Scale-Dependence of Halo Assembly Bias