Theory of the Kitaev model in a [111] magnetic field

TL;DR

This paper uses a variational approach to show that the field-induced spin liquid in the Kitaev honeycomb model is gapped and belongs to Kitaev's 16-fold way, clarifying its topological nature and phase transition characteristics.

Contribution

It introduces a variational method based on fractionalized excitations to identify the gapped topological phase in a magnetic field, resolving previous ambiguities about its gapless or gapped nature.

Findings

The field-induced spin liquid is gapped and topologically nontrivial.

The phase transitions between non-Abelian and Abelian liquids are characterized.

The effective field theory explains the apparent gapless behavior at criticality.

Abstract

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev's 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number $C=\pm 1$ transitions into an Abelian liquid with $C=\pm 4$. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.