Entanglement microscopy and tomography in many-body systems

Ting-Tung Wang, Menghan Song, Liuke Lyu, William Witczak-Krempa () and Zi Yang Meng ()
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Ting-Tung Wang: The University of Hong Kong
Menghan Song: The University of Hong Kong
Liuke Lyu: Université de Montréal
William Witczak-Krempa: Université de Montréal
Zi Yang Meng: The University of Hong Kong

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: Abstract Quantum entanglement uncovers the essential principles of quantum matter, yet determining its structure in realistic many-body systems poses significant challenges. Here, we employ a protocol, dubbed entanglement microscopy, to reveal the multipartite entanglement encoded in the full reduced density matrix of the microscopic subregion in spin and fermionic many-body systems. We exemplify our method by studying the phase diagram near quantum critical points (QCP) in 2 spatial dimensions: the transverse field Ising model and a Gross-Neveu-Yukawa transition of Dirac fermions. Our main results are: i) the Ising QCP exhibits short-range entanglement with a finite sudden death of the LN both in space and temperature; ii) the Gross-Neveu QCP has a power-law decaying fermionic LN consistent with conformal field theory (CFT) exponents; iii) going beyond bipartite entanglement, we find no detectable 3-party entanglement with our two witnesses in a large parameter window near the Ising QCP in 2d, in contrast to 1d. We further establish the singular scaling of general multipartite entanglement measures at criticality and present an explicit analysis in the tripartite case.

Date: 2025
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DOI: 10.1038/s41467-024-55354-z

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