Dynamical and Topological Properties of the Kitaev Model in a [111] Magnetic Field

TL;DR

This paper investigates the phase diagram and dynamical properties of the Kitaev honeycomb model under a [111] magnetic field, revealing topological, intermediate, and polarized phases with numerical evidence of non-Abelian anyons.

Contribution

It provides large-scale numerical analysis of the Kitaev model in a magnetic field, identifying phase transitions and characterizing topological excitations with dynamical signatures.

Findings

Confirmation of three distinct phases depending on field strength and exchange sign.

Observation of cubic scaling of the energy gap in the topological phase.

Numerical extraction of the quantum dimension of non-Abelian anyons.

Abstract

The Kitaev model exhibits a Quantum Spin Liquid hosting emergent fractionalized excitations. We study the Kitaev model on the honeycomb lattice coupled to a magnetic field along the [111] axis. Utilizing large scale matrix product based numerical models, we confirm three phases with transitions at different field strengths depending on the sign of the Kitaev exchange: a non-abelian topological phase at low fields, an enigmatic intermediate regime only present for antiferromagnetic Kitaev exchange, and a field-polarized phase. For the topological phase, we numerically observe the expected cubic scaling of the gap and extract the quantum dimension of the non-Abelian anyons. Furthermore, we investigate dynamical signatures of the topological and the field-polarized phase using a matrix product operator based time evolution method.