Measuring quantum entanglement in Kitaev quantum spin liquid

Quantum spin liquids possess long-ranged entangled topological order without symmetry breaking. Quantum entanglement is a fundamental property of the many body ground state wave function; it is however not directly measurable. In this work, our aim is to connect quantum entanglement with physical observables in the paradigmatic Kitaev spin liquid on a honeycomb lattice. Our central result is to show that through physical observables, we can reconstruct the quantum entanglement entropy. Furthermore, we show that both the entanglement entropy and the correlators capture the non-analytic behavior at quantum phase transitions at and away from the exactly solvable points when tuned by a magnetic field and by anisotropy of the bond interaction. Through this work, we provide a more intuitive understanding of quantum entanglement and highlight its role in detecting quantum phase transitions.