On the Entanglement Entropy in Gaussian cMERA

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

doi:10.1002/prop.202100093

Cited by 3 publications

(18 citation statements)

References 23 publications

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“…First, recall that the half-space EE for this theory does not violate the area law of entanglement. Following the results and discussions stated in [25], we note that a putative dual spacetime derived from the EE in Eq. (2.33) should be kept entire.…”

Section: Holography: Cmera and The Sharp Radial Cutoff Proposalmentioning

confidence: 74%

Entanglement Renormalization of a $T\bar{T}$-deformed CFT

Cardona,

Molina-Vilaplana

2022

Preprint

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In this work we use cMERA, a continuous tensor network, to study a T T -deformed scalar CFT on the line. We show that the entanglement renormalization flow implemented by a (Gaussian) cMERA captures some features which fit well with the known properties of the interacting theory. We discuss about the non-localities induced by the T T deformation at some length scales by computing the entanglement entropy on the cMERA optimized state. We find that the kind of non-locality generated by those terms can be considered as a mild-one, in the sense that it does not violate the area law of entanglement. In the context of the conjectured connection between cMERA and holography, we find that at first insight a finite bulk radius can be defined in the putative geometric dual description of cMERA. However, the entropy analysis contradicts the proposal that no geometry can be ascribed to the region outside this radial cutoff.

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Section: Holography: Cmera and The Sharp Radial Cutoff Proposalmentioning

confidence: 74%

Entanglement Renormalization of a $T\bar{T}$-deformed CFT

Cardona,

Molina-Vilaplana

2022

Preprint

View full text Add to dashboard Cite

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“…First, recall that the half-space EE for this theory does not violate the area law of entanglement. Following the results and discussions stated in [29], we note that a putative dual spacetime derived from the EE in eq. (2.33) should be kept entire.…”

Section: Jhep07(2022)092mentioning

confidence: 75%

“…For a half-space bipartition of the total space, the entanglement entropy of a state approximated by a Gaussian cMERA is given by [29]…”

Section: Entanglement Entropy and The Non-locality Of T Tmentioning

confidence: 99%

Entanglement renormalization of a $$ \mathrm{T}\overline{\mathrm{T}} $$-deformed CFT

Cardona

Molina-Vilaplana

2022

J. High Energ. Phys.

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In this work we use cMERA, a continuous tensor network, to find a Gaussian approximation to the ground state of a T$$ \overline{T} $$ T ¯ -deformed scalar CFT on the line, to first order in the deformation parameter. The result is used to find the correction to the correlators of scaling operators of the theory and to the entanglement entropy of a half-line. From the latter, we discuss the non-localities induced by the T$$ \overline{T} $$ T ¯ deformation at short length scales. We find that the kind of non-locality generated by those terms can be considered as a mild-one, in the sense that it does not violate the area law of entanglement. In the context of the conjectured connection between cMERA and holography, we find that at first insight a finite bulk radius can be defined in the putative geometric dual description of cMERA. However, the entropy analysis contradicts the proposal that no geometry can be ascribed to the region outside this radial cutoff.

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“…Then, using the properties of the trial wavefunctionals generated by the O(N ) icMERA circuit, we calculate the half space entanglement entropy by using the same techniques as in [32,33]. When considering a 1/N expansion, the entanglement entropy for B N is given by (see (4.53))…”

Section: Resultsmentioning

confidence: 99%

“…In order to sustain our calculation of entanglement entropy based on a Fisher metricinspired definition of a bond dimension, we have obtained the entanglement entropy by means of a parallel computation based solely on the Gaussian nature of the icMERA wavefunctional in the basis of non-linearly deformed fields which the method is based on and the results for the half space entropy in a Gaussian cMERA [33].…”

Section: Jhep04(2022)020mentioning

confidence: 99%

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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On the Entanglement Entropy in Gaussian cMERA

Cited by 3 publications

References 23 publications

Entanglement Renormalization of a $T\bar{T}$-deformed CFT

Entanglement Renormalization of a $T\bar{T}$-deformed CFT

Entanglement renormalization of a $$ \mathrm{T}\overline{\mathrm{T}} $$-deformed CFT

The large N limit of icMERA and holography

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