# Condensates of interacting non-Abelian $SO(5)_{N_f}$ anyons

## TL;DR

This paper investigates the condensation phenomena of $SO(5)_{N_f}$ anyons in a one-dimensional relativistic fermion model, revealing phase transitions and collective states characterized by parafermionic cosets.

## Contribution

It introduces a detailed analysis of $SO(5)_{N_f}$ anyon condensation and identifies the associated collective states and phase diagram in a low-dimensional fermionic system.

## Key findings

- Massive solitons form $SO(5)$ multiplets as $SO(5)_{N_f}$ anyons.
- Transitions from free anyons to collective states are controlled by magnetic fields.
- Generalized parafermionic cosets describe the collective phases.

## Abstract

Starting from a one-dimensional model of relativistic fermions with $SO(5)$ spin and $U(N_f)$ flavor degrees of freedom we study the condensation of $SO(5)_{N_f}$ anyons. In the low-energy limit the quasi-particles in the spin sector of this model are found to be massive solitons forming multiplets in the $SO(5)$ vector or spinor representations. The solitons carry internal degrees of freedom which are identified as $SO(5)_{N_f}$ anyons. By controlling the external magnetic fields the transitions from a dilute gas of free anyons to various collective states of interacting ones are observed. We identify the generalized parafermionic cosets describing these collective states and propose a low temperature phase diagram for the anyonic modes.