Entanglement susceptibilities and universal geometric entanglement entropy

TL;DR

This paper introduces entanglement susceptibilities to analyze how entanglement entropy varies with geometric deformations of the entangling surface, revealing universal contributions from non-smooth features across various quantum states.

Contribution

It formulates the concept of entanglement susceptibilities and derives their form for scale-invariant states, enabling the calculation of universal geometric contributions to entanglement entropy.

Findings

Derived the form of leading entanglement susceptibilities for conformal and Lifshitz states.

Identified universal contributions from corners, cones, and trihedral vertices.

Extended analysis to Renyi entropies.

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.