Entanglement Witness for Indistinguishable Electrons using Solid-State Spectroscopy

Abstract

Characterizing entanglement in quantum materials is crucial for advancing next-generation quantum technologies. Despite recent strides in witnessing entanglement in magnetic materials with distinguishable spin modes, quantifying entanglement in systems formed by indistinguishable electrons remains a formidable challenge. To solve this problem, we introduce a method to extract various four-fermion correlations by analyzing the nonlinearity in resonant inelastic x-ray scattering spectra. These correlations constitute the primary components of the cumulant two-particle reduced density matrix. We further derive bounds for its eigenvalues and demonstrate the linear scaling with fermionic entanglement depth, providing a reliable witness for entanglement. Using the material-relevant strongly correlated models as examples, we show how this entanglement witness can efficiently quantify multipartite entanglement across different phase regions, highlighting its advantage over quantum Fisher information.

28 pages, 15 figures

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Cited by in corpus (4)

• Strong long-wavelength electron-phonon coupling in Ta${}_2$Ni(Se,S)${}_5$
• General recipe for immediate entanglement death-birth transitions via Bell states: environmental Heisenberg exchange as an example
• Witnessing Spin-Orbital Entanglement using Resonant Inelastic X-Ray Scattering
• Accelerating Resonant Spectroscopy Simulations Using Multi-Shifted Bi-Conjugate Gradient