Entanglement susceptibility: Area laws and beyond

TL;DR

This paper introduces entanglement susceptibility, a new measure derived from 2-Renyi entropy expansion, to explain area laws and their violations in quantum many-body systems, especially near criticality.

Contribution

It proposes the novel concept of entanglement susceptibility and links it to area laws and boundary correlation functions in local gapped Hamiltonians.

Findings

Entanglement susceptibility explains area law emergence.

Quantifies violations near gapless points.

Provides an exact series expansion for 2-Renyi entropy.

Abstract

Generic quantum states in the Hilbert space of a many body system are nearly maximally entangled whereas low energy physical states are not; the so-called area laws for quantum entanglement are widespread. In this paper we introduce the novel concept of entanglement susceptibility by expanding the 2-Renyi entropy in the boundary couplings. We show how this concept leads to the emergence of area laws for bi-partite quantum entanglement in systems ruled by local gapped Hamiltonians. Entanglement susceptibility also captures quantitatively which violations one should expect when the system becomes gapless. We also discuss an exact series expansion of the 2-Renyi entanglement entropy in terms of connected correlation functions of a boundary term. This is obtained by identifying Renyi entropy with ground state fidelity in a doubled and twisted theory.