Quantum Fisher Information as a Thermal Probe in Frustrated Magnets through Insights from Quantum Spin Ice

Quantum Fisher information (QFI) is a measure of multipartite entanglement accessible via inelastic neutron scattering. Here we demonstrate that QFI reveals thermal and dynamical properties of quantum spin ice (QSI), a three-dimensional quantum spin liquid with fractionalized excitations. By developing a multi-directed loop update quantum Monte Carlo algorithm, along with exact diagonalization and gauge mean-field theory, we compute the QFI for the pyrochlore lattice. The temperature and momentum dependence of QFI maps the phase diagram, distinguishing the ferromagnetic ordered phase, its critical region, the zero-flux QSI, and the $\pi$-flux QSI. QFI also captures two crossover scales: from trivial paramagnet to classical spin ice, then to QSI. We discuss the $\pi$-flux QSI in light of experiments on cerium-based pyrochlores. Our results suggest that QFI not only detects entanglement but also serves as a sensitive thermal and dynamical probe for frustrated quantum magnets.