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.

• Received 8 March 2022
• Revised 19 September 2022
• Accepted 19 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.125145