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Hyperuniform many-particle systems are characterized by a structure factor$S({\mathbf{k}})$ that is precisely zero as $|\mathbf{k}|\rightarrow0$; andstealthy hyperuniform systems have $S({\mathbf{k}})=0$ for the finite range $0< |{\mathbf{k}}| \le K$, called the "exclusion region." Through a process ofcollective-coordinate optimization, energy-minimizing disordered stealthyhyperuniform systems of moderate size have been made to high accuracy, andtheir novel physical properties have shown great promise. However, minimizing$S(\mathbf{k})$ in the exclusion region is computationally intensive as thesystem size becomes large. In this Letter, we present an improved methodologyto generate such states using double-double precision calculations on GPUs thatreduces the deviations from zero within the exclusion region by a factor ofapproximately $10^{30}$ for systems sizes more than an order of magnitudelarger. We further show that this ultra-high accuracy is required to drawconclusions about their corresponding characteristics, such as the nature ofthe associated energy landscape and the presence or absence of Andersonlocalization, which might be masked, even when deviations are relatively small.

Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties