Quantum entanglement and quantum geometry measured with inelastic X-ray scattering

Abstract

Using inelastic X-ray scattering (IXS), we experimentally investigate the quantum geometry and quantum information in the large-gap insulator, LiF. Using sum rules for the density-density response function measured in IXS, we compute the quantum Fisher information of the equilibrium density matrix of LiF associated with density perturbations. Next, by exploiting universal relations between the quantum Fisher information, the optical conductivity, and the quantum metric tensor, we extrapolate the diagonal $(h,k,l)=(1,0,0)$ component of the quantum metric of LiF, known as the quantum weight. We compare our results to recently-proposed bounds on the quantum weight and find that the quantum weight in LiF comes close to saturating a theoretical upper bound, showing that quantum-mechanical delocalization plays an important role even in ionic insulators. Our work serves as a proof-of-principle that IXS techniques can be used to quantify state-of-the-art quantum geometric quantities of materials, and establishes the quantum Fisher information as an experimentally-accessible generalization of quantum geometry to real materials.

v2: accepted version. 7 pages, 3 figures

References in corpus (24)

• Measuring multipartite entanglement via dynamic susceptibilities
• Superfluidity and Quantum Geometry in Twisted Multilayer Systems
• Band geometry of fractional topological insulators
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Essay: Where Can Quantum Geometry Lead Us?
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• The effective fine structure constant of freestanding graphene measured in graphite
• Geometry and response of Lindbladians
• Quantum geometry induced nonlinear transport in altermagnets
• Geometric stability of topological lattice phases
• Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
• Witnessing entanglement in quantum magnets using neutron scattering
• Fundamental bound on topological gap
• Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)
• The quantum geometric origin of capacitance in insulators
• Intrinsic anomalous Hall conductivity in a nonuniform electric field
• Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling
• Polarization fluctuations in insulators and metals: New and old theories merge
• Quantum Quench and $f$-Sum Rules on Linear and Non-linear Conductivities
• Generalized $f$-Sum Rules and Kohn formulas on Non-linear Conductivities
• Universal relation between energy gap and dielectric constant
• Spectral Density and Sum Rules for Second-Order Response Functions
• Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
• Topological Density Correlations in a Fermi Gas

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• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Quantum geometric bounds in spinful systems with trivial band topology
• Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric
• Electronic bounds in magnetic crystals
• Imaginary Time Formalism for Causal Nonlinear Response Functions
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
• Spinon excitations and spin correlations in the one-dimensional quantum magnet $\beta$-VOSO${}_4$ probed by Raman spectroscopy