Anyon polarons as a window into competing phases of the Kitaev honeycomb model under a Zeeman field

TL;DR

This paper investigates how Zeeman fields influence anyon quasiparticles in the Kitaev honeycomb model, revealing critical points where different quasiparticles become gapless, indicating phase transitions and symmetry breaking.

Contribution

It provides a comprehensive analysis of the spectra of all three quasiparticle sectors under Zeeman perturbation, challenging previous theories of the intermediate phase.

Findings

Fermions and visons become gapless at similar critical fields.

In the ferromagnetic case, this leads to a direct transition to a polarized state.

In the antiferromagnetic case, the intermediate phase involves spontaneous symmetry breaking.

Abstract

We compute the spectra of anyon quasiparticles in all three super-selection sectors of the Kitaev model (i.e., visons, fermions and bosons), perturbed by a Zeeman field away from its exactly solvable limit, to gain insights on the competition of its non-abelian spin-liquid with other nearby phases, such as the mysterious intermediate state observed in the antiferromagnetic model. Both for the ferro- and antiferro-magnetic models we find that the fermions and visons become gapless at nearly identical critical Zeeman couplings. In the ferromagnetic model this is consistent with a direct transition into a polarized state. In the anti-ferromagnetic model this implies that previous theories of the intermediate phase viewed as a spin liquid with a different fermion Chern number are inadequate, as they presume that the vison gap does not close. In the antiferromagnetic model we also find that a bosonic quasiparticle becomes gapless at nearly the same critical field as the fermions and visons. This boson carries the quantum numbers of an anti-ferromagnetic order parameter, suggesting that the intermediate phase has spontaneously broken symmetry with this order.