Non-Gaussianity of entanglement entropy and correlations of composite operators

Iso, Satoshi; Mori, Takato; Sakai, Kyosuke

doi:10.1103/physrevd.103.125019

Cited by 11 publications

(16 citation statements)

References 79 publications

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“…See the proof in Appendix B. See also the discussions in Section 4B and Section 4C in our previous paper [43]. There is a single twist for a 1-loop diagram.…”

Section: Z M Gauge Theory On Feynman Diagramsmentioning

confidence: 86%

“…In this section, we first summarize our previous works in [42,43], and then introduce a new concept of the generalized 1PI in order to unify the contributions to EE from propagators and vertices.…”

Section: Summary Of Previous Workmentioning

confidence: 99%

“…Corresponding to three different channels of the opening, s, t, and u, there are three different configurations of fluxes and contributions to EE, respectively. If different quantum numbers are assigned to these three channels, we can utilize a method of auxiliary fields and EE is given by a sum of propagator contributions of three different auxiliary fields as shown in [43]. If composite operators propagating three channels are mixed like the φ 4 -theory, we cannot use the method of auxiliary fields, but from diagrammatic analysis (see Appendix B), we can show that it is written in terms of a correlation function of composite operators.…”

Section: Vertex Contributions To Ee and Generalized 1pimentioning

confidence: 99%

“…In this paper, we will investigate EE in interacting field theories based on the Wilsonian picture of renormalization combined with our previous works [42,43] based on the Z M gauge theory on Feynman diagrams. In [42], we succeeded to extract two particular contributions to EE in interacting field theories: one is the Gaussian contributions written in terms of renormalized two-point correlation functions in the two-particle irreducible (2PI) formalism.…”

Section: Introductionmentioning

confidence: 99%

“…Another set of important contributions comes from classical vertices, which reflects non-Gaussianity of the vacuum wave function. In [43], we showed that the vertex contributions can be interpreted as contributions from renormalized two-point correlation functions of composite operators. These results are obtained by evaluating EE in the notion of the Z M gauge theory on Feynman diagrams, whose picture is derived from the replica method of EE (the number of replicas n is replaced by n = 1/M).…”

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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“…See the proof in Appendix B. See also the discussions in Section 4B and Section 4C in our previous paper [43]. There is a single twist for a 1-loop diagram.…”

Section: Z M Gauge Theory On Feynman Diagramsmentioning

confidence: 86%

Section: Summary Of Previous Workmentioning

confidence: 99%

Section: Vertex Contributions To Ee and Generalized 1pimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Wilsonian Effective Action and Entanglement Entropy

2021

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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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Universal entanglement signatures of quantum liquids as a guide to fermionic criticality

2023

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An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) shows a violation of the area-law in real-space entanglement entropy of a subsystem, believed to be a signature of the ground state of a gapless quantum critical system of interacting fermions. Here, we apply a $T=0$ renormalisation group approach to the FL, unveiling the long-wavelength quantum fluctuations from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga-Luttinger liquid (TLL) reveals a universal logarithmic violation of the area-law in gapless electronic liquids, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to classify the gapped quantum liquids emergent from the destabilisation of the Fermi surface by RG relevant quantum fluctuations arising from backscattering processes.

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Non-Gaussianity of entanglement entropy and correlations of composite operators

Cited by 11 publications

References 79 publications

Wilsonian Effective Action and Entanglement Entropy

Wilsonian Effective Action and Entanglement Entropy

The large N limit of icMERA and holography

Universal entanglement signatures of quantum liquids as a guide to fermionic criticality

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