Ultralow-temperature spin kinetics of strongly hybridized electro-nuclear excitations in LiHoF 4

Recent cavity-magnon-polariton (CMP) spectroscopy of the quantum Ising magnet LiHoF 4 represents a remarkable experimental achievement, providing high-fidelity baseline spectra of electro-nuclear spin transitions. However, the interpretation of these results using a standard single-ion mean-field theory (MFT) predictably falls short in describing many-body dynamic correlations, leaving several pronounced anomalies unexplained: double peaks of dissipation near the quantum critical point (QCP), bell-shaped transition linewidths, and the collectivization of discrete transitions below the critical field. In this paper, we formulate a theoretical framework based on the low-temperature spin kinetics framework. By incorporating a chemical potential for electro-nuclear excitations (µ EN ) and deriving the dynamic susceptibility via the Non-Equilibrium Statistical Operator (NSO) method, we provide a unified analytical resolution for these anomalies, offering a complete thermodynamic description of the strongly hybridized spin dynamics.