# Valence bond fluctuations in the Kitaev spin model

## TL;DR

This paper introduces valence bond fluctuations as a new way to characterize quantum spin liquids and their phase transitions in the Kitaev model, revealing a universal scaling law and robustness under magnetic fields.

## Contribution

It presents valence bond fluctuations as a novel tool to analyze quantum spin liquids, establishing their relation to entanglement entropy and phase transitions in the Kitaev model.

## Key findings

- Valence bond fluctuations scale identically to entanglement entropy.
- They can locate phase transitions between gapped and gapless phases.
- The fluctuations remain a robust indicator under magnetic field effects.

## Abstract

We introduce valence bond fluctuations, or bipartite fluctuations associated to bond-bond correlation functions, to characterize quantum spin liquids and their entanglement properties. Using analytical and numerical approaches, we find an identical scaling law between valence bond fluctuations and entanglement entropy in the two-dimensional Kitaev spin model and in one-dimensional chain analogues. We also show how these valence bond fluctuations can locate quantum phase transitions between the three gapped and the gapless Majorana semi-metal phases in the honeycomb model. We then study the effect of a uniform magnetic field along the 111 direction opening a gap in the intermediate phase which becomes topological. We still obtain a robust signal to characterize the transitions towards the three gapped phases. The linear scaling behavior of such bipartite fluctuations in two dimensions is also distinguishable from the one in the Neel magnetic state.