# Interrelations among frustration-free models via Witten's conjugation

### Submission summary

 As Contributors: Hosho Katsura · Dirk Schuricht · Jurriaan Wouters Preprint link: scipost_202104_00026v2 Date accepted: 2021-08-11 Date submitted: 2021-07-20 21:38 Submitted by: Schuricht, Dirk Submitted to: SciPost Physics Core Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

We apply 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.

Published as SciPost Phys. Core 4, 027 (2021)

We thank the referee for his/her positive report.
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We thank the referee for his/her report, in particular for acknowledging the usefulness of our manuscript in providing a unified framework to treat seemingly different models. With this in mind, we view the simplicity of the treatment of the individual systems as an advantage. Also, our aim was not to provide an encyclopedic paper picking all low-hanging fruit, as noted in the last paragraph of Section 7.

We have revised our manuscript to address the two points explicitly raised: (1) We now mention in the introduction that MPS methods yield correlation functions, and (2) we revised Remark 3 to avoid the impression that MPS are hard to deal with. We also added a footnote to link our findings to the general framework of injective MPS.

### List of changes

Summary of changes:
-penultimate paragraph of the introduction: added a remark that correlation functions can be obtained via MPS methods
-rephrased Remark 3 in line 594
-added footnote 6 on page 24 to discuss properties of injective MPS