# Tuning topological orders by a conical magnetic field in the Kitaev model

## TL;DR

This paper demonstrates how a conical magnetic field can tune the topological order and anyon excitations in the Kitaev model, revealing new phases with different topological properties and excitations.

## Contribution

It introduces a method to control topological phases in the Kitaev model using a conical magnetic field, identifying a novel C=4 topological order and the persistence of the C=1 phase.

## Key findings

- A new C=4 topological order with Abelian anyons is induced at intermediate fields.
- The C=1 Ising-topological order persists and revives at certain field ranges.
- The study employs a Z2 mean field theory and variational quantum Monte Carlo methods.

## Abstract

We show that a conical magnetic field ${\bf H}=(1,1,1)H$ can be used to tune the topological order and hence anyon excitations of the $\mathrm{Z_2}$ quantum spin liquid in the isotropic antiferromagnetic Kitaev model. A novel topological order, featured with Chern number $C=4$ and Abelian anyon excitations, is induced in a narrow range of intermediate fields $H_{c1}\leq H\leq H_{c2}$. On the other hand, the $C=1$ Ising-topological order with non-Abelian anyon excitations, is previously known to be present at small fields, and interestingly, is found here to survive up to $H_{c1}$, and revive above $H_{c2}$, until the system becomes trivial above a higher field $H_{c3}$. The results are obtained by devoloping and applying a $\mathrm{Z_2}$ mean field theory, that works at zero as well as finite fields, and the associated variational quantum Monte Carlo.