Entanglement Entropy in Quantum Field Theory

Dear Colleagues,

At the beginning of the 1990s, a series of works involving C. Callan, C. Holzhey, F. Larsen and F. Wilczek highlighted the universal properties of a measure of entanglement known as entanglement entropy. Their studies considered quantum corrections to black hole entropy and saw entropy in the context of geometry and gravity. Those results admitted also a more general interpretation as describing the quantum entanglement associated with quantum critical points, which in 1+1 dimensions are described by the conformal field theory (CFT). Drawing on the powerful mathematical structures underpinning CFT, it has since been possible to obtain many more universal results for a wide range of entanglement measures, ranging from the entanglement and Rényi entropies to the logarithmic negativity. There have been many contributions to this development, with the work of P. Calabrese and J. L. Cardy in 2004 playing a pivotal role in bringing these ideas to the low-dimensional quantum field theory (QFT) community. Later, this CFT viewpoint has been related to a picture emerging from the AdS/CFT correspondence, leading to the well-known relationship between entanglement entropy and the area minimal surfaces pioneered by S. Ryu and T. Takayanagi in 2006. Another frontier in this investigation has been the challenge of progressing beyond CFT, to describing universal properties of entanglement in the near-critical region described by massive QFT. For interacting integrable 1+1-dimensional QFTs, the branch point twist field approach, introduced by J.L. Cardy, O. A. Castro-Alvaredo and B. Doyon in 2007, has become a leading method to do just that. By relating entanglement measures to correlation functions of local fields, it has been possible to encapsulate the intricacies of entanglement measures into the problem of expanding multi-point correlation functions in terms of different parameters. This viewpoint has been further generalised to describe more recent entanglement measures such as the symmetry resolved entanglement, introduced by Goldstein and Sela in 2018, in terms of a composite twist field picture. The objective of this Special Issue is to bring together original contributions to this active area of research.

Dr. Olalla Castro-Alvaredo
Dr. David X. Horvath
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• entanglement measures
• quantum field theory
• conformal field theory
• quantum spin chains
• holography
• symmetry
• numerics
• exact results