Systems of particles interacting via stealthy potentials, a family of soft, long-ranged, isotropic pair potentials, possess infinitely degenerate disordered hyperuniform classical ground states of fundamental and practical interest, highlighted by their novel optical and mechanical properties. The configurational dimensionality of the ground-state manifold depends on a dimensionless parameter $\chi$ that measures the number of independently constrained degrees of freedom in a ground state. Starting from a wide class of initial two-dimensional point configurations, we study the evolution of trajectories of the collective-coordinate optimization procedure to their corresponding disordered stealthy hyperuniform ground states as a function of $\chi$ within the disordered regime ($0<\chi <1/2$). Initial conditions studied span a wide class of disordered systems, including antihyperuniform, nonhyperuniform, and hyperuniform ones. The evolution of the trajectories is quantified by computing a translational order metric and configurational proximity metric as a function of the computational time for selected values of $\chi$ within the disordered regime. The rate at which trajectories approach the ground-state manifold is fastest for those evolved from hyperuniform states and slowest for those evolved from antihyperuniform states. We observe that ground-state ensembles with distinct pair statistics are sampled by different initial conditions across a broad range of $\chi$ and that these pair statistics are generally effected by higher-order spatial correlations characterizing the initial condition. Learning how to manipulate initial conditions in the optimization procedure to target different portions of the ground-state manifold enables one to explore structurally unique stealthy ground states with designed short- up to intermediate-ranged spatial correlations for the purposes of materials discovery.

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• Exotic phases of matter