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From knots to crystals: Machine-learned potentials for self-assembling topological solitons in liquid crystals

Arunkumar Bupathy1,*, Darian Hall2,3, Ivan I. Smalyukh1,2,4,5,†, Gerardo Campos-Villalobos6,7, Rodolfo Subert6, and Marjolein Dijkstra1,6,‡

  • *Contact author: abupathy@hiroshima-u.ac.jp
  • †Contact author: ivan.smalyukh@colorado.edu
  • ‡Contact author: m.dijkstra@uu.nl
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Phys. Rev. Research 8, 023235 – Published 1 June, 2026

DOI: https://doi.org/10.1103/fbxl-n36k

Abstract

Knotted fields in classical and quantum systems have long been recognized for their nontrivial topologies and particlelike 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 scales and timescales 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.

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Phys. Rev. Research 8, 023235– Published 1 June, 2026
  • Received 30 November 2025
  • Accepted 3 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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