Stealthy hyperuniform systems in increasing spatial dimensions and their connections to hard sphere problems

Stealthy hyperuniform systems are ones for which the structure factor S(k) is zero for all wave-vectors with magnitude below a cutoff K, i.e. S(k<K) = 0. Trivially, all crystals are stealthy hyperuniform, but disordered stealthy hyperuniform systems also exist. Several properties of stealthy hyperuniform systems can be predicted by noting that standard hard spheres have a pair correlation function g(r) which prevents overlap, such that g(r<R) = 0, suggesting that stealthy hyperuniform systems can be treated as hard spheres in Fourier space [1]. While this correspondence has been made and tested in dimensions d=1-4, here we investigate the phase behavior as the dimension increases and make direct connections to standard hard sphere problems. Notably, for hard spheres in Fourier space, the highest density packing, the freezing transition, and the ground state manifold are very different from that of standard hard spheres. To aid in this investigation, we use recently developed numerical techniques [2] that enhance the collective coordinate procedure, enabling large disordered stealthy hyperuniform systems in arbitrary dimensions with high accuracy.



[1] S. Torquato, G. Zhang, F. H. Stillinger, “Ensemble Theory for Stealthy Hyperuniform Disordered Ground States”, Phys. Rev. X 5, 021020 (2015)



[2] P.K. Morse, J. Kim, P.J. Steinhardt, S. Torquato, ``Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties.'' Phys. Rev. Res., 5, 033190, (2023)