From Knots to Crystals: Machine-Learned Potentials for Self-Assembling Topological Solitons in Liquid Crystals

TL;DR

This paper develops machine-learned coarse-grained potentials to simulate and understand stable knotted solitons in liquid crystals, enabling large-scale modeling of their assembly and dynamics.

Contribution

It introduces a machine learning approach to create effective potentials that accurately reproduce experimental topological soliton assemblies in liquid crystals.

Findings

Accurately reproduces experimentally observed heliknoton assemblies.

Enables simulations at larger length and time scales than traditional models.

Provides a transferable framework for other topological solitons.

Abstract

Knotted fields in classical and quantum systems have long been recognized for their non-trivial topologies and particle-like behavior, but practical applications have been limited by the difficulty of stabilizing them. Recently, stable knotted solitonic textures--heliknotons--were discovered in chiral liquid crystals, forming adaptive crystal assemblies via elastic distortion-mediated interactions. We use machine learning to develop single-site coarse-grained potentials that accurately capture these chiral anisotropic effective interactions. The resulting potentials accurately reproduce experimentally observed heliknoton assemblies and enable simulations at length and time scales far beyond the range of fine-grained continuum models. This general framework is readily transferable to other topological solitons, providing a powerful route to understand, predict, and ultimately control their collective behavior and dynamics.