  One-dimensional bosons interacting via a soft-shoulder potential are
investigated at zero temperature. The flatness of the potential at short
distances introduces a typical length, such that, at relatively high densities
and sufficiently strong interactions, clusters are formed, even in the presence
of a completely repulsive potential. We evaluate the static density response
function of this system across the transition from the liquid to the cluster
liquid phases. Such quantity reveals the density modulations induced by a weak
periodic external potential, and is maximal at the clustering wavevector. It is
known that this response function is proportional to the static structure
factor in the classical regime at high temperature, while for this
zero-temperature quantum systems, we extract it from the dynamical structure
factor evaluated with quantum Monte Carlo methods.
