Entanglement of skeletal regions

TL;DR

This paper investigates the entanglement entropy of skeletal regions with no volume in quantum many-body systems, revealing new universal behaviors and scaling laws distinct from traditional bulk entanglement.

Contribution

It introduces the concept of skeletal entanglement, providing non-perturbative bounds and exploring its behavior across various quantum states and critical points.

Findings

Skeletal entanglement exhibits unique topological and corner contributions.

Discovery of strict area-law scaling for metals.

Identification of skeletal topological entanglement entropy.

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). In this work, we study the EE of skeletal regions that have \textit{no} volume, such as a line in 2d. We show that skeletal entanglement displays new behavior compared to its bulk counterpart, and leads to distinct universal quantities. We provide non-perturbative 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. We discuss the possibility of a continuum description involving the fusion of defect operators. Finally, we outline open questions relating to other systems, and measures such as the logarithmic negativity.