Entanglement susceptibilities and universal geometric entanglement entropy

Abstract

The entanglement entropy (EE) can measure the entanglement between a spatial subregion and its complement, which provides key information about quantum states. Here, rather than focusing on specific regions, we study how the entanglement entropy changes with small deformations of the entangling surface. This leads to the notion of entanglement susceptibilities. These relate the variation of the EE to the geometric variation of the subregion. We determine the form of the leading entanglement susceptibilities for a large class of scale invariant states, such as groundstates of conformal field theories, and systems with Lifshitz scaling, which includes fixed points governed by disorder. We then use the susceptibilities to derive the universal contributions that arise due to non-smooth features in the entangling surface: corners in 2d, as well as cones and trihedral vertices in 3d. We finally discuss the generalization to Renyi entropies.

11 pages (single-column), 3 figures, 1 table

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Cited by in corpus (8)

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• Generalizing the entanglement entropy of singular regions in conformal field theories
• Relating bulk to boundary entanglement
• Shape dependence of renormalized holographic entanglement entropy
• Geometric entanglement in integer quantum Hall states
• CFT correlators from shape deformations in Cubic Curvature Gravity
• The entanglement entropy of the quantum Hall edge and its geometric contribution
• Cluster tomography in percolation