Capacity of entanglement and volume law

TL;DR

This paper explores the capacity of entanglement in systems with volume law entanglement, analyzing its behavior in various scalar field theories and discussing implications for holographic duals.

Contribution

It provides analytical and numerical evidence for volume law scaling of capacity of entanglement across different models and discusses its relation to other entanglement measures.

Findings

Capacity of entanglement obeys volume law in studied setups

Capacity correlates with entanglement entropy and Renyi entropies

Results suggest implications for holographic duality

Abstract

We investigate various aspects of capacity of entanglement in certain setups whose entanglement entropy becomes extensive and obeys a volume law. In particular, considering geometric decomposition of the Hilbert space, we study this measure both in the vacuum state of a family of non-local scalar theories and also in the squeezed states of a local scalar theory. We also evaluate field space capacity of entanglement between interacting scalar field theories. We present both analytical and numerical evidences for the volume law scaling of this quantity in different setups and discuss how these results are consistent with the behavior of other entanglement measures including Renyi entropies. Our study reveals some generic properties of the capacity of entanglement and the corresponding reduced density matrix in the specific regimes of the parameter space. Finally, by comparing entanglement entropy and capacity of entanglement, we discuss some implications of our results on the existence of consistent holographic duals for the models in question.