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Updated: Sep 6, 2025

Three and Four-Dimensional Visualization and Analysis Approaches to Study Vertebrate Axial Elongation and Segmentation
Published on: February 28, 2021
Entanglement of Skeletal Regions
Clément Berthiere1,2, William Witczak-Krempa1,2
1Université de Montréal, C. P. 6128, Succursale Centre-ville, Montréal, QC, Canada, H3C 3J7.
Abstract:
The entanglement entropy (EE) encodes key properties of quantum many-body systems. It is usually calculated for subregions of finite volume (or area in 2D). Here, we study the EE of skeletal regions that have no volume, such as a line in 2D. We show that skeletal entanglement displays new behavior compared with its bulk counterpart, and leads to distinct universal quantities. We provide nonperturbative bounds for the skeletal area-law coefficient of a large family of quantum states. We then explore skeletal scaling for the toric code, conformal bosons and Dirac fermions, Lifshitz critical points, and Fermi liquids. We discover signatures including skeletal topological EE, novel corner terms, and strict area-law scaling for metals. These findings suggest that skeletal entropy serves as a measure for the range of entanglement. Finally, we outline open questions relating to other systems and measures such as the logarithmic negativity.
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