Especially in one dimension, models with discrete and continuous symmetries display different physical properties, starting from the existence of long-range order. In this work, we that, by adding topological frustration, an antiferromagnetic $XYZ$ spin chain, characterized by a discrete local symmetry, develops a region in parameter space that mimics the features of models with continuous symmetries. For instance, frustration closes the mass gap and we describe a continuous crossover between ground states with different quantum numbers, a finite (Fermi) momentum for low energy states, and the disappearance of the finite order parameter. Moreover, we observe nontrivial ground-state degeneracies, nonvanishing chirality, and a singular foliation of the ground-state fidelity. Across the boundary between this chiral region and the rest of the phase diagram, any discontinuity in the energy derivatives vanishes in the thermodynamic limit.

中文翻译：

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用离散模型模拟连续对称模型

尤其是在一维上，具有离散和连续对称性的模型表现出不同的物理性质，这从长程有序的存在开始。在这项工作中，我们认为，通过添加拓扑挫折，反铁磁$X是Z$以离散局部对称为特征的自旋链在参数空间中形成一个区域，该区域模仿具有连续对称性的模型的特征。例如，挫折缩小了质量差距，我们描述了具有不同量子数的基态之间的连续交叉，低能态的有限（费米）动量，以及有限阶参数的消失。此外，我们观察到非平凡的基态退化、不消失的手性和基态保真度的奇异叶状结构。在这个手性区域和相图其余部分之间的边界上，能量导数的任何不连续性都会在热力学极限中消失。