Bosonization in $R$-paraparticle Luttinger models

Alternative theories of quantum statistics provide an avenue for exploring novel physics beyond bosons and fermions, yet experimental verification of their existence in nature proves a challenging task. Among these theories, it has recently been suggested that $R$-parastatistics can be realized as quasiparticle excitations in many-body systems. In this paper, we build on this idea by showing that signatures of $R$-parastatistics can be observed as flavor-charge separation in 1D systems. We consider a generalized version of the Luttinger model and show that bosonization persists when the $R$-paraparticles have fermi-surface-like structures. These $R$\textit{-parafermions} can satisfy generalized exclusion principles beyond conventional Pauli's. We show that density waves of all $R$-parafermions can always be bosonized, but flavor waves act like bosons only for a certain sublcass of $R$-parafermions. We derive the conditions for bosonization by analyzing the LM spectrum, showing that bosonization applies only to low-temperature systems. Signatures of flavor-charge separation then become apparent as distinct dispersion profiles when we turn on inter-particle interactions. This points to potential observations of flavor-charge separation in 1D systems that host emergent $R$-paraparticles.