Contributor info: Prof. Hosho Katsura

Hosho Katsura, Dirk Schuricht

SciPost Phys. Core 8, 052 (2025) · published 15 August 2025 | Toggle abstract · pdf

We consider the valence bond solid (VBS) state built of singlet pairs of fundamental representations and projected onto adjoint representations of the exceptional Lie group G$_2$. The two-point correlation function in the VBS state is non-vanishing only for nearest neighbours, but possesses finite string order. We construct a parent Hamiltonian for the VBS state, which constitutes the G$_2$ analog of the famous AKLT chain.

Jurriaan Wouters, Fabian Hassler, Hosho Katsura, Dirk Schuricht

SciPost Phys. Core 5, 008 (2022) · published 8 February 2022 | Toggle abstract · pdf

We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin--Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral $\mathbb{Z}_3$ axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.

Jurriaan Wouters, Hosho Katsura, Dirk Schuricht

SciPost Phys. Core 4, 027 (2021) · published 14 October 2021 | Toggle abstract · pdf

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.