Quantifying and controlling entanglement in the quantum magnet Cs$_2$CoCl$_4$

TL;DR

This study demonstrates that inelastic neutron scattering can be used to experimentally detect and quantify entanglement in quantum spin systems, specifically in Cs$_2$CoCl$_4$, using entanglement witnesses like QFI, one-tangle, and two-tangle.

Contribution

It introduces a model-independent protocol for entanglement detection in quantum materials using INS and validates it on Cs$_2$CoCl$_4$ with theoretical comparisons.

Findings

QFI is a robust experimental entanglement probe

INS-based entanglement measurement is feasible in quantum magnets

Entanglement properties can be inferred from neutron scattering data

Abstract

The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs$_2$CoCl$_4$, a close realization of the $S=1/2$ transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one- and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.