# Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice

## TL;DR

This paper extends the Kitaev honeycomb model with four-spin interactions, revealing a rich phase diagram with vison crystals, a $ ext{pi}$-flux spin liquid, and Lifshitz transitions, supported by Monte Carlo simulations.

## Contribution

It introduces a new extended Kitaev model that maintains integrability and explores its complex phase diagram with novel vison crystal phases.

## Key findings

- Identification of five distinct vison crystal phases.
- Discovery of a symmetric $ ext{pi}$-flux spin liquid with Majorana Fermi surface.
- Finite-temperature Monte Carlo results on specific heat and vison structure factor.

## Abstract

We introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and hence the integrability of the original model. The extended model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric $\pi$-flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. We discuss possible experimental signatures and, in particular, present finite-temperature Monte Carlo calculations of the specific heat and the static vison structure factor. We argue that our extended model emerges naturally from generic perturbations to the Kitaev honeycomb model.