Inherent Structures for Soft Long-Range Interactions in Two-Dimensional Many-Particle Systems

TL;DR

This study explores the inherent structures of two-dimensional many-particle systems with a $k$-space overlap potential, revealing their stealthy, hyperuniform nature, structural features, and the particle rearrangements needed to achieve ideal stealthiness.

Contribution

It provides a detailed analysis of inherent structures, their properties, and transition pathways, advancing understanding of collective-coordinate potentials and stealthy disordered states.

Findings

Inherent structures show varying degrees of stealthiness and hyperuniformity.

Structural features include five-particle rings, grain boundaries, and defects.

Small local rearrangements can transform RSA configurations into stealthy ground states.

Abstract

We generate inherent structures, local potential-energy minima, of the "$k$-space overlap potential" in two-dimensional many-particle systems using a cooling and quenching simulation technique. The ground states associated with the $k$-space overlap potential are stealthy ({\it i.e.,} completely suppress single scattering of radiation for a range of wavelengths) and hyperuniform ({\it i.e.,} infinite wavelength density fluctuations vanish). However, we show via quantitative metrics that the inherent structures exhibit a range of stealthiness and hyperuniformity depending on the fraction of degrees of freedom that are constrained. Inherent structures in two dimensions typically contain five-particle rings, wavy grain boundaries, and vacancy-interstitial defects. The structural and thermodynamic properties of inherent structures are relatively insensitive to the temperature from which they are sampled, signifying that the energy landscape is relatively flat and devoid of deep wells. Using the nudged-elastic-band algorithm, we construct paths from ground-state configurations to inherent structures and identify the transition points between them. In addition, we use point patterns generated from a random sequential addition (RSA) of hard disks, which are nearly stealthy, and examine the particle rearrangements necessary to make the configurations absolutely stealthy. We introduce a configurational proximity metric to show that only small local, but collective, particle rearrangements are needed to drive initial RSA configurations to stealthy disordered ground states. These results lead to a more complete understanding of the unusual behaviors exhibited by the family of "collective-coordinate" potentials to which the $k$-space overlap potential belongs.