Instantons and Entanglement Entropy

Abstract

We would like to put the area law -- believed to by obeyed by entanglement entropies in the ground state of a local field theory -- to scrutiny in the presence of non-perturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton effects are well understood, including $U(1)$ gauge theory in 2+1 dimensions and false vacuum decay in ${\varphi }^4$ theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.

29 pages, 4 figures, typos corrected, substantially revised, published version

References in corpus (5)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• General entanglement scaling laws from time evolution
• Entanglement Entropy in the O(N) model
• Bulk Emergence and the RG Flow of Entanglement Entropy
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole

Cited by in corpus (5)

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• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• On the Entanglement Entropy of Maxwell Theory: A Condensed Matter Perspective
• Supersymmetry breaking, brane dynamics and Swampland conjectures
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach