Non-Gaussian entanglement renormalization for quantum fields

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

doi:10.1007/jhep07(2020)149

Cited by 25 publications

(71 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand current approaches to continuous tensor networks such as e.g. cMERA (continuous MERA) are limited to free theories (see however [32][33][34][35][36] for recent progress beyond free CFTs). Therefore, in order to draw conclusions about a genuine holography, we need to develop a tensor network-like formalism applicable to continuous and interacting, holographic CFTs.…”

Section: Jhep07(2021)016 1 Introductionmentioning

confidence: 99%

Holographic path-integral optimization

Boruch

Caputa

et al. 2021

J. High Energ. Phys.

View full text Add to dashboard Cite

In this work we elaborate on holographic description of the path-integral optimization in conformal field theories (CFT) using Hartle-Hawking wave functions in Anti-de Sitter spacetimes. We argue that the maximization of the Hartle-Hawking wave function is equivalent to the path-integral optimization procedure in CFT. In particular, we show that metrics that maximize gravity wave functions computed in particular holographic geometries, precisely match those derived in the path-integral optimization procedure for their dual CFT states. The present work is a detailed version of [1] and contains many new results such as analysis of excited states in various dimensions including JT gravity, and a new way of estimating holographic path-integral complexity from Hartle-Hawking wave functions. Finally, we generalize the analysis to Lorentzian Anti-de Sitter and de Sitter geometries and use it to shed light on path-integral optimization in Lorentzian CFTs.

show abstract

Section: Jhep07(2021)016 1 Introductionmentioning

confidence: 99%

Holographic path-integral optimization

Boruch

Caputa

et al. 2021

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…This method also allows for other further applications. For example, it is worth to mention that the approach of NLCT can be applied to fermionic field theories [24]. Despite the method can be formulated in any dimension and/or type of fermion, in [24] we only considered the case of two-dimensional Dirac fermions.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…For example, it is worth to mention that the approach of NLCT can be applied to fermionic field theories [24]. Despite the method can be formulated in any dimension and/or type of fermion, in [24] we only considered the case of two-dimensional Dirac fermions. This results specially well suited to analyze the Gross-Neveu model (GN) [29].…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…In the perturbative regime, for the self interacting scalar theory, given a NLCT of the form π φ n , it is possible to systematically obtain a diagrammatic interpretation of the contributions to the n-point correlation functions yielded by the ansatz. This gives account of the non-Gaussian contributions to the correlators [10,24]. As it is shown in these references, the diagrammatic content of the correlation functions yielded by NLCT trial states adds up a much larger class of Feynman diagrams than the usual "cactus"-like ones of the Gaussian approach.…”

Section: Entanglement Entropy In φ Theorymentioning

confidence: 93%

See 1 more Smart Citation

Entanglement entropy: non-Gaussian states and strong coupling

Fernandez-Melgarejo

Molina-Vilaplana

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

“…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%

Wilsonian Effective Action and Entanglement Entropy

2021

View full text Add to dashboard Cite

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.

show abstract

Non-Gaussian entanglement renormalization for quantum fields

Cited by 25 publications

References 37 publications

Holographic path-integral optimization

Holographic path-integral optimization

Entanglement entropy: non-Gaussian states and strong coupling

Wilsonian Effective Action and Entanglement Entropy

Contact Info

Product

Resources

About