论文标题
二面体液晶中的任何人缺陷编织和自发性手性对称性破裂
Anyonic defect braiding and spontaneous chiral symmetry breaking in dihedral liquid crystals
论文作者
论文摘要
二面体（$ k $ - '）液晶（DLC）是显微镜组成粒子的组件，它们表现出$ k $ - 倍离散的离散旋转和反射对称性。概括了夜间液晶中的半全能缺陷，二维$ k $ - dlcs可以寄主分数拓扑费$ \ pm m/k $的宿主点缺陷。从通用的微观模型开始，我们根据Ginzburg-Landau和Landau-Brazovskii-Swift-Hohenberg理论，对DLC进行了统一的DLC的统一流体动力描述。在此框架的基础上，我们在粒子和连续模拟中都证明了绝热编织方案如何通过适当的边界条件实现，可以模仿经典系统中的任何互联型交换行为。平均场理论的分析解决方案和模拟进一步预测了抗对准DLC中新型自发性手性对称性破坏过渡，这与在粒子模拟中观察到的模式进行了定量一致。
Dihedral ('$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 $\pm m/k$. Starting from a generic microscopic model, we derive a unified hydrodynamic description of DLCs with aligning or anti-aligning 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 both particle and continuum 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 anti-aligning DLCs, in quantitative agreement with the patterns observed in particle simulations.
