Measurement of the Quantum Fisher Information and Electronic Entanglement in Insulators

ORAL

Abstract

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).

*This work was primarily supported by the Center for Quantum Sensing and Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0021238. P.A. gratefully acknowledges additional support from the EPiQS program of the Gordon and Betty Moore Foundation, Grant No. GBMF9452. The theoretical work of B.B. on wave-function geometry was additionally supported by the Alfred P. Sloan Foundation, and the National Science Foundation under Grant No. DMR-1945058. IXS measurements at the Advanced Photon Source were supported by DOE Grant No. DE-AC02-06CH11357. D.B. was supported in part by the Barry Goldwater Scholarship and Excellence in Education Foundation, and the Astronaut Scholarship Foundation.

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Publication: [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).

Presenters

  • David Bałut

    • University of Illinois at Urbana-Champaign

Authors

  • David Bałut

    • University of Illinois at Urbana-Champaign

  • Barry Bradlyn

    • University of Illinois at Urbana-Champaign
    • University of Illinois Urbana-Champaign

  • Peter Abbamonte

    • University of Illinois at Urbana-Champaign