Temporal Entanglement in Quantum Field Theory

TL;DR

This paper introduces a method to compute temporal entanglement entropy in quantum field theory, revealing complex, oscillatory behavior and universal features related to the mass spectrum, analogous to spatial entanglement.

Contribution

It generalizes spatial entanglement measures to the temporal domain using a branch point twist field approach, providing new insights into time-dependent quantum correlations.

Findings

Temporal entanglement entropy is complex and oscillatory.

Temporal and spatial entropies share universal features.

A quasiparticle picture helps interpret temporal entanglement results.

Abstract

In this paper I propose a branch point twist field approach to computing a temporal entropy, that is, an entanglement measure across different time regions, as opposed to the usual spacial measures. I discuss how the shift to time-dependence manifests in form factor calculations and how the generalization of the spacial measures to temporal ones reproduces expected features of the temporal entanglement: the entropy is complex, oscillatory and reminiscent of the evolution of entanglement following a global quench. Considering the temporal von Neumann entropy, I argue that spacial and temporal entropies are two sides of the same coin. They both encapsulate universal information about the theory, in particular its mass spectrum. Also in both cases, a quasiparticle picture can be employed to interpret results. Some qualitative features of this version of temporal entropy, such as its similarity to the entanglement entropy after a global quench, are shared with the known temporal measures.