Resilience of the topological phases to frustration

Vanja Marić,Domagoj Kuić,Salvatore Marco Giampaolo,Fabio Franchini

doi:10.1038/s41598-021-86009-4

Vanja Marić, Domagoj Kuić + Show 2 more

Open Access

https://doi.org/10.1038/s41598-021-86009-4

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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.

Highlights

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
We have presented an analysis of the effects of frustrated boundary conditions on different topologically ordered phases characterizing one-dimensional models
We have focused on the onedimensional Cluster-Ising model with an odd number of spins and periodic boundary conditions

Summary

Introduction

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. The effects of the topological frustration can be even stronger coming to the point of preventing the creation of any local o rder[17] and inducing a change in the nature of the macroscopic phases, and related phase transitions, in the system[18]. Behind this violation of one of the main prescriptions of Landau theory is that FBCs induce a geometrical frustration in the s ystem[19,20].

Objectives

Conclusion