Simulating continuous symmetry models with discrete ones

TL;DR

This paper demonstrates that by introducing topological frustration, a discrete symmetry antiferromagnetic XYZ spin chain can exhibit properties akin to continuous symmetry models, including gap closure and continuous ground state crossover.

Contribution

It shows how topological frustration induces continuous symmetry-like features in a discrete symmetry spin chain, bridging the gap between discrete and continuous models.

Findings

Frustration closes the mass gap.

Continuous crossover between ground states.

Disappearance of finite order parameter.

Abstract

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.