Entanglement entropy: non-Gaussian states and strong coupling

Fernandez-Melgarejo, Jose J.; Molina-Vilaplana, Javier

doi:10.1007/jhep02(2021)106

Cited by 13 publications

(26 citation statements)

References 31 publications

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“…We conjecture that the IR part of EE in interacting field theories is given by a sum of all vertex contributions in the Wilsonian effective action. In this context, it is interesting to look at the relation to the variational method of EE [28][29][30]51]. In this approach, EE of interacting field theories is expressed in terms of a non-Gaussian deformation of the Gaussian vacuum wave function.…”

Section: Discussionmentioning

confidence: 99%

“…On the other hand, we have little understanding of EE in general interacting QFTs, apart from exactly solvable cases [20] or some supersymmetric theories [12,13,[21][22][23]. EE in interacting theories are discussed in perturbative [24,25], nonperturbative [26][27][28][29][30][31][32], lattice [33][34][35][36][37], or in terms of variational trial wave functions [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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Wilsonian Effective Action and Entanglement Entropy

2021

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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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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wilsonian Effective Action and Entanglement Entropy

2021

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“…where 𝜇 is a variational mass parameter that in the free case equals the bare mass m of the theory. Remarkably, in [17], a cMERA circuit based on the quadratic entangler (19) was used to study the self-interacting 𝜙 4 scalar theory. This model has a mass gap and flows to a free theory in the IR, where the IR ground state is exactly a Gaussian wavefunctional.…”

Section: Gaussian Cmeramentioning

confidence: 99%

“…In this case the entangling surface is A ⟂ = ℝ d−1 and its area will be denoted by |A ⟂ |. According to the heat kernel result ( 14), the entanglement entropy of the half space can be written as [18,19]…”

Section: Entanglement Entropy In Gaussian Cmeramentioning

confidence: 99%

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On the Entanglement Entropy in Gaussian cMERA

Fernandez-Melgarejo

Molina-Vilaplana

2021

Fortschritte der Physik

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The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA) consists of a variational method which carries out a real space renormalization scheme on the wavefunctionals of quantum field theories. In this work we calculate the entanglement entropy of the half space for a free scalar theory through a Gaussian cMERA circuit. We obtain the correct entropy written in terms of the optimized cMERA variational parameter, the local density of disentanglers. Accordingly, using the entanglement entropy production per unit scale, we study local areas in the bulk of the tensor network in terms of the differential entanglement generated along the cMERA flow. This result spurs us to establish an explicit relation between the cMERA variational parameter and the radial component of a dual AdS geometry through the Ryu-Takayanagi formula. Finally, we argue that the entanglement entropy for the half space can be written as an integral along the renormalization scale whose measure is given by the Fisher information metric of the cMERA circuit. Consequently, a straightforward relation between AdS geometry and the Fisher information metric is also established.

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The large N limit of icMERA and holography

Fernandez-Melgarejo

Molina-Vilaplana

2022

J. High Energ. Phys.

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In this work, we compute the entanglement entropy in continuous icMERA tensor networks for large N models at strong coupling. Our results show that the 1/N quantum corrections to the Fisher information metric (interpreted as a local bond dimension of the tensor network) in an icMERA circuit, are related to quantum corrections to the minimal area surface in the Ryu-Takayanagi formula. Upon picking two different non-Gaussian entanglers to build the icMERA circuit, the results for the entanglement entropy only differ at subleading orders in 1/GN, i.e., at the structure of the quantum corrections in the bulk. The fact that the large N part of the entropy can be always related to the leading area term of the holographic calculation is very suggestive. These results, constitute the first tensor network calculations at large N and strong coupling simultaneously, pushing the field of tensor network descriptions of the emergence of dual spacetime geometries from the structure of entanglement in quantum field theory.

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Entanglement entropy: non-Gaussian states and strong coupling

Cited by 13 publications

References 31 publications

Wilsonian Effective Action and Entanglement Entropy

Wilsonian Effective Action and Entanglement Entropy

On the Entanglement Entropy in Gaussian cMERA

The large N limit of icMERA and holography

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