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 bonanza shown by these variational 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 ϕ4 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.

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Wilsonian Effective Action and Entanglement Entropy

Symmetry ◽

10.3390/sym13071221 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1221

Author(s):

Satoshi Iso ◽

Takato Mori ◽

Katsuta Sakai

Keyword(s):

Renormalization Group ◽

Gauge Theory ◽

Effective Action ◽

Correlation Functions ◽

Entanglement Entropy ◽

Feynman Diagrams ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Non Gaussian

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.

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On the renormalization of entanglement entropy

AAPPS Bulletin ◽

10.1007/s43673-021-00032-1 ◽

2021 ◽

Vol 31 (1) ◽

Author(s):

Jin-Yi Pang ◽

Jiunn-Wei Chen

Keyword(s):

Field Theory ◽

Black Hole ◽

Scalar Field ◽

Entanglement Entropy ◽

Black Hole Entropy ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Replica Trick ◽

Dimensional Spacetime

AbstractThe renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λϕ4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.

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Swing surfaces and holographic entanglement beyond AdS/CFT

Journal of High Energy Physics ◽

10.1007/jhep12(2020)064 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Luis Apolo ◽

Hongliang Jiang ◽

Wei Song ◽

Yuan Zhong

Keyword(s):

Black Holes ◽

Lorentz Invariance ◽

Entanglement Entropy ◽

Three Dimensional ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Asymptotically Flat ◽

Infinite Dimensional ◽

Holographic Entanglement Entropy

Abstract We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat3/BMSFT and (W)AdS3/WCFT. Flat3/BMSFT is a candidate of holography for asymptotically flat three- dimensional spacetimes, while (W)AdS3/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.

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Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/42/50/504006 ◽

2009 ◽

Vol 42 (50) ◽

pp. 504006 ◽

Cited By ~ 23

Author(s):

Olalla A Castro-Alvaredo ◽

Benjamin Doyon

Keyword(s):

Entanglement Entropy ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field

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Galois conjugation and multiboundary entanglement entropy

Journal of High Energy Physics ◽

10.1007/jhep12(2020)045 ◽

2020 ◽

Vol 2020 (12) ◽

Cited By ~ 1

Author(s):

Matthew Buican ◽

Rajath Radhakrishnan

Keyword(s):

Physical Meaning ◽

Entanglement Entropy ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Galois Action ◽

Topological Quantum ◽

Link Complements ◽

Link Complement ◽

Modular Data

Abstract We revisit certain natural algebraic transformations on the space of 3D topological quantum field theories (TQFTs) called “Galois conjugations.” Using a notion of multiboundary entanglement entropy (MEE) defined for TQFTs on compact 3-manifolds with disjoint boundaries, we give these abstract transformations additional physical meaning. In the process, we prove a theorem on the invariance of MEE along orbits of the Galois action in the case of arbitrary Abelian theories defined on any link complement in S3. We then give a generalization to non-Abelian TQFTs living on certain infinite classes of torus link complements. Along the way, we find an interplay between the modular data of non-Abelian TQFTs, the topology of the ambient spacetime, and the Galois action. These results are suggestive of a deeper connection between entanglement and fusion.

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Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

Zeitschrift für Naturforschung A ◽

10.1515/zna-1985-0717 ◽

1985 ◽

Vol 40 (7) ◽

pp. 752-773

Author(s):

H. Stumpf

Keyword(s):

Composite Particle ◽

Particle Interaction ◽

High Energy ◽

Field Theories ◽

Quantum Field Theories ◽

Statistical Interpretation ◽

Quantum Field ◽

Mapping Procedure ◽

Effective Dynamics ◽

Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

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Categorification of algebraic quantum field theories

Letters in Mathematical Physics ◽

10.1007/s11005-021-01371-8 ◽

2021 ◽

Vol 111 (2) ◽

Author(s):

Marco Benini ◽

Marco Perin ◽

Alexander Schenkel ◽

Lukas Woike

Keyword(s):

Universal Algebra ◽

Finite Groups ◽

Physical Interpretation ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Algebraic Quantum

AbstractThis paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

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