Measuring entanglement entropy and its topological signature for phononic systems

Zhi-Kang Lin, Yao Zhou, Bin Jiang, Bing-Quan Wu, Li-Mei Chen, Xiao-Yu Liu, Li-Wei Wang, Peng Ye () and Jian-Hua Jiang ()
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Zhi-Kang Lin: Soochow University
Yao Zhou: Sun Yat-sen University
Bin Jiang: University of Science and Technology of China
Bing-Quan Wu: Soochow University
Li-Mei Chen: Sun Yat-sen University
Xiao-Yu Liu: Soochow University
Li-Wei Wang: Soochow University
Peng Ye: Sun Yat-sen University
Jian-Hua Jiang: Soochow University

Nature Communications, 2024, vol. 15, issue 1, 1-8

Abstract: Abstract Entanglement entropy is a fundamental concept with rising importance in various fields ranging from quantum information science, black holes to materials science. In complex materials and systems, entanglement entropy provides insight into the collective degrees of freedom that underlie the systems’ complex behaviours. As well-known predictions, the entanglement entropy exhibits area laws for systems with gapped excitations, whereas it follows the Gioev-Klich-Widom scaling law in gapless fermion systems. However, many of these fundamental predictions have not yet been confirmed in experiments due to the difficulties in measuring entanglement entropy in physical systems. Here, we report the experimental verification of the above predictions by probing the nonlocal correlations in phononic systems. We obtain the entanglement entropy and entanglement spectrum for phononic systems with the fermion filling analog. With these measurements, we verify the Gioev-Klich-Widom scaling law. We further observe the salient signatures of topological phases in entanglement entropy and entanglement spectrum.

Date: 2024
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DOI: 10.1038/s41467-024-45887-8

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