Temporal Entanglement in Quantum Field Theory

Abstract:In this paper I propose a branch point twist field approach to computing the temporal entropy, that is, an entanglement measure across different time regions, as opposed to the usual spacial measures. Considering only the ground state of a gapped theory, I discuss how the shift to time-dependence manifests in form factor calculations. I show that 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. This picture connects features of the temporal entropy with those of the spacial entropy following a quantum quench.

15 pages. This is the published version, which includes an additional Section 6

arXiv:2603.20765 [hep-th]

(or arXiv:2603.20765v2 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2603.20765 Focus to learn more arXiv-issued DOI via DataCite

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