Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case

TL;DR

This paper investigates how local and topological frustrations interact in the 1D ANNNI spin chain, revealing a phase with two nearly independent excitations and proposing a novel quasi-particle interpretation.

Contribution

It demonstrates the significant impact of boundary-induced topological frustration on the ANNNI model and introduces a new quasi-particle perspective for understanding its phases.

Findings

Boundary conditions influence frustration effects

Ground state hosts two nearly independent excitations

Proposes a novel quasi-particle interpretation

Abstract

We consider the effects of the competition between different sources of frustration in 1D spin chains through the analysis of the paradigmatic ANNNI model, which possesses an extensive amount of frustration of local origin due to the competition between nearest and next-to-nearest neighbor interactions. An additional, non-extensive amount of topological frustration can be added by applying suitable boundary conditions, and we show that this seemingly subdominant contribution significantly affects the model. Choosing periodic boundary conditions with an {\it even} number of sites not divisible by 4 and using the entanglement entropy as a probe, we demonstrate that in one of the model's phases, the ground state can be characterized as hosting two (almost) independent excitations. Thus, not only do we show an intriguing interplay between different types of frustration, but also manage to propose a non-trivial quasi-particle interpretation for it.