# Constructive approach for frustration-free models using Witten's conjugation

### Submission summary

 As Contributors: Dirk Schuricht Arxiv Link: https://arxiv.org/abs/2005.12825v1 (pdf) Date submitted: 2020-05-27 Submitted by: Schuricht, Dirk Submitted to: SciPost Physics Discipline: Physics Subject area: Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

We extend Witten's conjugation argument [Nucl. Phys. B 202, 253 (1982)] to spin chains, where it allows us to derive frustration-free systems and their exact ground states from known results. We particularly focus on $\mathbb{Z}_p$-symmetric models, with the Kitaev and Peschel--Emery line of the axial next-nearest neighbour Ising (ANNNI) chain being the simplest examples. The approach allows us to treat two $\mathbb{Z}_3$-invariant frustration-free parafermion chains, recently derived by Iemini et al. [Phys. Rev. Lett. 118, 170402 (2017)] and Mahyaeh and Ardonne [Phys. Rev. B 98, 245104 (2018)], respectively, in a unified framework. We derive several other frustration-free models and their exact ground states, including $\mathbb{Z}_4$- and $\mathbb{Z}_6$-symmetric generalisations of the frustration-free ANNNI chain.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 2005.12825v1 on 27 May 2020