Entanglement Entropy: Non-Gaussian States and Strong Coupling

Abstract

In this work we provide a method to study the entanglement entropy for non-Gaussian states that minimize the energy functional of interacting quantum field theories at arbitrary coupling. To this end, we build a class of non-Gaussian variational trial wavefunctionals with the help of exact nonlinear canonical transformations. The calculability \emph{bonanza} shown by these variational \emph{ansatze} allows us to compute the entanglement entropy using the prescription for the ground state of free theories. In free theories, the entanglement entropy is determined by the two-point correlation functions. For the interacting case, we show that these two-point correlators can be replaced by their nonperturbatively corrected counterparts. Upon giving some general formulae for general interacting models we calculate the entanglement entropy of half space and compact regions for the ${\varphi }^4$ scalar field theory in 2D. Finally, we analyze the rôle played by higher order correlators in our results and show that strong subadditivity is satisfied.

arXiv commentV1: 23 pp, 3 figures. V2: 25 pp, 3 figures (typos fixed and comments added, to be published in JHEP)

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• Quantifying fermionic interactions from the violation of Wick's theorem
• A post-Gaussian approach to dipole symmetries and interacting fractons
• Exact renormalization group for wave functionals
• The Large $N$ Limit of icMERA and Holography
• On the Entanglement Entropy in Gaussian cMERA
• Non-Gaussian Variational Wavefunctions for Interacting Bosons on the Lattice