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Bosonization in $R$-paraparticle Luttinger models

Dennis F. Salinel, Kristian Hauser A. Villegas

Abstract

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.

Bosonization in $R$-paraparticle Luttinger models

Abstract

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 -parastatistics can be realized as quasiparticle excitations in many-body systems. In this paper, we build on this idea by showing that signatures of -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 -paraparticles have fermi-surface-like structures. These \textit{-parafermions} can satisfy generalized exclusion principles beyond conventional Pauli's. We show that density waves of all -parafermions can always be bosonized, but flavor waves act like bosons only for a certain sublcass of -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 -paraparticles.

Paper Structure

This paper contains 12 sections, 63 equations, 2 figures.

Table of Contents

  1. Introduction
  2. R-paraparticles
  3. Formulation
  4. R-parafermions
  5. R-parafermion bosonization
  6. Density wave bosonization and flavor-charge separation
  7. Flavor wave bosonization
  8. Equivalence spectrum
  9. Interacting systems
  10. Potential experimental realization
  11. Summary and Discussion
  12. R-parabosons

Figures (2)

  • Figure 1: Summary of main results. (a.) Occupation statistics of different types of $R$-parafermions (solid line) and $R$-parabosons (dashed line). The single-mode partition functions of the latter are obtained using Eq. \ref{['eq:a1']}. (b) Partition functions of the noninteracting $R$-paraparticle LMs in the $R$-parafermion and boson basis. (c) Sketch of expected dispersions of $R$-parafermionic quasiparticles obtained from an underlying spinor TG gas.
  • Figure 2: Dispersion relation of $R$-parafermionic LM with (a) contact, (b) Yukawa, and (c) screened interactions, where in (b) and (c), we used $g=1$. We have set $v_F = 1$ for all calculations. For all cases, we see distinct differences between the flavor-wave (denoted by the broken line) and density-wave dispersions (in solid lines). The corresponding density wave velocity is obtained as the slope of the solid curves at $q = 0$.