Simulating continuous symmetry models with discrete ones

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 which 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 non-trivial ground state degeneracies, non-vanishing 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.