# Anyon polarons as a window into the competing phases of the Kitaev-Gamma-Gamma' model

## TL;DR

This paper explores how anyon gap closures in the Kitaev honeycomb model with perturbations reveal phase transitions into various magnetic orders and spin-liquid states, providing insights into the model's complex phase diagram.

## Contribution

It introduces a method to understand phase transitions via anyon gap closures in the Kitaev-Gamma-Gamma' model, linking them to specific competing phases and critical coupling values.

## Key findings

- Anyon gap closings signal phase transitions into zigzag, stripy, 120°, and incommensurate spiral phases.
- In certain perturbations, the spin liquid coexists with magnetic order due to selective gap closures.
- The study aligns theoretical gap-closing points with numerical phase boundaries.

## Abstract

We investigate the dispersions of anyon quasi-particles in the Kitaev honeycomb spin-liquid perturbed by $\Gamma$ and $\Gamma'$ couplings in order to understand phase transitions into competing states through anyon gap-closing instabilities. We demonstrate how anyon gap closings allow to understand phase transitions into a plethora of previously identified competing phases -- including zigzag, stripy, $120^\circ$, and incommensurate spiral phases -- and are in agreement with numerical studies not only on the nature of the phases, but also on the specific critical values of $\Gamma$ and $\Gamma'$ couplings. Remarkably, when the anti-ferromagnetic Kitaev model is perturbed by an ferromagnetic $\Gamma$ interaction, we find that the single-vison and fermion gaps remain open while the gap of a magnon-like local boson vanishes, implying that the resulting state has coexistence of a spontaneous broken symmetry and the fractionalization pattern of the Kitaev spin liquid. The magnetic long-range order could be either a stripy antiferromagnet or an incommensurate spiral, depending on the sign of $\Gamma'$.