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arXiv:2310.05870 · Physical Review Letters

Detecting Multipartite Entanglement Patterns Using Single-Particle Green’s Functions

Rajesh K. Malla, Andreas Weichselbaum, Tzu-Chieh Wei, Robert Konik

Published Dec 31, 2024• 5 citations

Abstract

We present a protocol for detecting multipartite entanglement in itinerant many-body electronic systems using single-particle Green's functions. To achieve this, we first establish a connection between the quantum Fisher information and single-particle Green's functions by constructing a set of witness operators built out of single electron creation and destruction operators in a doubled system. This set of witness operators is indexed by a momentum k. We compute the quantum Fisher information for these witness operators and show that for thermal ensembles it can be expressed as an autoconvolution of the single-particle spectral function. We then apply our framework to a one-dimensional fermionic system to showcase its effectiveness in detecting entanglement in itinerant electron models. We observe that the detected entanglement level is sensitive to the wave vector associated with witness operator. Our protocol will permit detecting entanglement in many-body systems using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, two spectroscopies that measure the single-particle Green's function. It offers the prospect of the experimental detection of entanglement through spectroscopies beyond the established route of measuring the dynamical spin response.

DOI: 10.1103/physrevlett.133.260202

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_3

CeIr

_2

O

_9

and used to directly test for entanglement of the electronic orbitals between neighboring Ir sites. We find the entanglement can be detected if we account for the expected symmetries, parity, and electron number conservation, of the dimer system. We also consider the roles that the incident and outgoing x-ray polarizations and the incident photon energy play in entanglement detection. Our protocol provides a new handle for entanglement detection in quantum materials.

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