Resilience of the topological phases to frustration

TL;DR

This paper investigates how frustrated boundary conditions affect topological phases in one-dimensional spin models, finding that these phases remain robust despite boundary-induced frustration, suggesting topological phases are generally resilient to such effects.

Contribution

It demonstrates that topological order phases in 1D systems are unaffected by frustrated boundary conditions, providing evidence for their robustness.

Findings

Topological phases are stable under frustrated boundary conditions.

Frustration does not induce phase transitions in topological phases.

Topological order is resilient to boundary-induced frustration.

Abstract

Recently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the presence of frustrated boundary conditions can destroy the local magnetic orders presented by the models when different boundary conditions are taken into account and induce novel phase transitions. Motivated by these results, we analyze the effects of the introduction of frustrated boundary conditions on several models supporting (symmetry protected) topological orders, and compare our results with the ones obtained with different boundary conditions. None of the topological order phases analyzed are altered by this change. This observation leads naturally to the conjecture that topological phases of one-dimensional systems are in general not affected by topological frustration.