Measurement of the Quantum Fisher Information and Electronic Entanglement in Insulators

The Quantum Fisher Information (QFI) has emerged as an experimentally accessible probe of quantum geometry in condensed matter systems and a witness to entanglement in spin chains [1-2]. However, relating the QFI to electronic entanglement has remained an open question. In this talk, I will show that in non-interacting models of insulators, the QFI is lower bounded by eigenvalues of the reduced density matrix associated with translationally invariant partitions. As an instructive example, I will present this analysis for the SSH model. I will conclude by presenting an experimental measurement of the QFI in ionic insulator LiF and covalent insulator Diamond, showing that both satisfy theoretical bounds with the QFI in diamond larger than in LiF. Using results from quantum geometry, I attribute this difference in the QFI between the two insulators to the extent of electronic delocalization.

[1] D. Bałut, B. Bradlyn, and P. Abbamonte, “Quantum entanglement and quantum geometry measured with inelastic x-ray scattering,” Phys. Rev. B 111, 125161 (2025). 

[2] D. Bałut, X. Guo, N. de Vries, D. Chaudhuri, B. Bradlyn, P. Abbamonte, and P. W. Phillips, “Quantum Fisher information reveals UV–IR mixing in the strange metal,” Physica C: Superconductivity and its Applications 625, 1354750 (2025).