Phase diagram of the $\mathbb{Z}_3$-Fock parafermion chain with pair hopping

We study a tight binding model of \mathbb{Z}_3ℤ3-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge \boldsymbol{c=2}𝐜=2, and two gapless phases with central charge \boldsymbol{c=1}𝐜=1. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.