Solving one-dimensional paraparticle models via bosonization

Abstract

Bosonization is a method of solving interacting one dimensional many-body systems by transforming fermionic operators into bosonic ones and rewriting the system Hamiltonian in the bosonized basis. In this study, we generalize the bosonization framework to include a general class of paraparticles, that is, particle species with nontrivial statistics and thermodynamic behaviors distinct from bosons and fermions. We show that for the paraparticle Tomonaga and Luttinger models, the paraparticle-boson transformation is exactly the same as the fermion-boson transformation. Specifically, the generalization occurs under the assumption of the existence of a parafermi sea. We present specific paraparticle species where flavor-charge separation is observed, and provide a first example in which a paraparticle model can be solved in the presence of interactions.