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

Abstract

We study a tight binding model of ${\mathbb{Z}}_3$-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 $c=2$, and two gapless phases with central charge $c=1$. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.

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• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Many-body localization of ${\mathbb{Z}}_3$ Fock parafermions
• Disorder effects in the ${\mathbb{Z}}_3$ Fock parafermion chain
• Overlap of parafermionic zero modes at a finite distance
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Engineering a Josephson junction chain for the simulation of the clock model
• Noninteracting tight-binding models for Fock parafermions
• Parastatistics in Interacting Periodic Chains Revealed by Peierls Phase Twists and Shifted Conformal Towers