Quantum Fisher Information as a Thermal and Dynamical Probe in Frustrated Magnets: insights from Quantum Spin Ice

Quantum Fisher information (QFI) is a novel measure of multipartite quantum entanglement that can be measured in inelastic neutron scattering (INS) experiments. We demonstrate that the QFI can be used to understand the thermal and dynamical properties of quantum magnets by focusing on the pyrochlore lattice model of quantum spin ice (QSI). Combining a newly developed multi-directed-loop quantum Monte Carlo algorithm with exact diagonalization, we compute the momentum- and temperature-resolved QFI across the global phase diagram. In particular, we find that the QFI can clearly distinguish the ferromagnetic ordered phase, the thermal critical region above it, as well as two distinct QSI phases, namely zero-flux and $\pi$-flux QSI. It also reveals the two crossover temperatures: from a trivial paramagnet to classical spin ice, and at a lower temperature from classical spin ice into QSI. We will discuss the implications and some potential interesting experiments, particularly for the $\pi$-flux regime, in light of ongoing measurements on Ce-based pyrochlore magnets. Our results establish QFI not only as an entanglement witness but also as a sensitive probe of thermal and dynamical properties in quantum magnets directly connectable to INS.