# On critical properties of Berry curvature in Kitaev honeycomb model

## TL;DR

This paper investigates the Berry curvature in the Kitaev honeycomb model, revealing how it behaves across topological phase transitions and providing insights into the model's critical properties.

## Contribution

It introduces an analytical approach to study Berry curvature in the Kitaev model, especially near phase transitions, using a Fermionisation technique and a time-reversal breaking term.

## Key findings

- Berry curvature shows non-critical behavior in different phases.
- First derivative of curvature exhibits critical behavior at transition points.
- Analysis enhances understanding of topological phase transitions in the model.

## Abstract

We analyse the Kitaev honeycomb model, by means of the Berry curvature with respect to Hamiltonian parameters. We concentrate on the ground-state vortex-free sector, which allows us to exploit an appropriate Fermionisation technique. The parameter space includes a time-reversal breaking term which provides an analytical headway to study the curvature in phases in which it would otherwise vanish. The curvature is then analysed in the limit in which the time-reversal-symmetry-breaking perturbation vanishes. This provides remarkable information about the topological phase transitions of the model. A non-critical behaviour is found in the Berry curvature itself, which shows a distinctive behaviour in the different phases. The analysis of the first derivative shows a critical behaviour around the transition point.