Anyonic Defect Braiding and Spontaneous Chiral Symmetry Breaking in Dihedral Liquid Crystals

Abstract

Dihedral (“k-atic”) liquid crystals (DLCs) are assemblies of microscopic constituent particles that exhibit k-fold discrete rotational and reflection symmetries. Generalizing the half-integer defects in nematic liquid crystals, two-dimensional k-atic DLCs can host point defects of fractional topological charge ±m/k. Starting from a generic microscopic model, we derive a unified hydrodynamic description of DLCs with aligning or antialigning short-range interactions in terms of Ginzburg-Landau and Landau-Brazovskii-Swift-Hohenberg theories for a universal complex order-parameter field. Building on this framework, we demonstrate in particle simulations how adiabatic braiding protocols, implemented through suitable boundary conditions, can emulate anyonic exchange behavior in a classical system. Analytic solutions and simulations of the mean-field theory further predict a novel spontaneous chiral symmetry-breaking transition in antialigning DLCs, in quantitative agreement with the patterns observed in particle simulations.