Interrelations among frustration-free models via Witten's conjugation

We apply Witten's conjugation argument [1] to spin chains, where it allows us to derive frustration-free systems and their exact ground states from known results. We particularly focus on 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 Z(3)-invariant frustration-free parafermion chains, recently derived by Iemini et al. [2] and Mahyaeh and Ardonne [3], respectively, in a unified framework. We derive several other frustration-free models and their exact ground states, including Z(4)- and Z(6)-symmetric generalisations of the frustration-free ANNNI chain.

Automated summary

By utilizing Witten's conjugation argument, frustration-free systems and their exact ground states can be derived from known results in spin chains, focusing particularly on Z(p)-symmetric models. This approach allows for a unified framework in treating various frustration-free models, including those recently derived by Iemini et al. and Mahyaeh and Ardonne. Additionally, several other frustration-free models and their exact ground states, such as Z(4)- and Z(6)-symmetric generalisations of the ANNNI chain, can be derived using this method.