Detecting Entanglement via Split Spectroscopy in Many-Body Systems

Quantum entanglement is recognized as a fundamental resource in quantum information processing and is essential for understanding quantum many-body physics. However, experimentally detecting entanglement, particularly in many-particle quantum states, remains a significant challenge. Here, we propose split spectroscopy as an experimentally feasible technique for detecting entanglement of eigenstates in quantum many-body systems. We demonstrate the split spectroscopy exhibits a single delta-function peak if and only if the investigated eigenstate is triseparable. Our framework is illustrated using two paradigmatic spin models that undergo quantum phase transitions. Furthermore, we show that the spectral entropy serves as a powerful indicator of quantum phase transitions and captures the scaling behavior of entanglement. Finally, we present an experimental protocol using Rydberg atom arrays.