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

by Jurriaan Wouters, Hosho Katsura, Dirk Schuricht

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

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