Critical and noncritical long-range entanglement in Klein-Gordon fields

S. Marcovitch*, A. Retzker, M. B. Plenio, B. Reznik

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We investigate the entanglement between two spatially separated intervals in the vacuum state of a free one-dimensional Klein-Gordon field by means of explicit computations in the continuum limit of the linear harmonic chain. We demonstrate that the entanglement, which we quantify by the logarithmic negativity, is finite with no further need for renormalization. We find that in the critical regime, the quantum correlations are scale invariant as they depend only on the ratio of distance to length. They decay much faster than the classical correlations as in the critical limit long-range entanglement decays exponentially for separations larger than the size of the blocks, while classical correlations follow a power-law decay. With decreasing distance of the blocks, the entanglement diverges as a power law in the distance. The noncritical regime manifests richer behavior, as the entanglement depends both on the size of the blocks and on their separation. In correspondence with the von Neumann entropy also long-range entanglement distinguishes critical from noncritical systems.

Original languageEnglish
Article number012325
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number1
StatePublished - 6 Aug 2009


FundersFunder number
Engineering and Physical Sciences Research CouncilEP/E045049/1


    Dive into the research topics of 'Critical and noncritical long-range entanglement in Klein-Gordon fields'. Together they form a unique fingerprint.

    Cite this