scholarly journals Physical states in the canonical tensor model from the perspective of random tensor networks

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Gaurav Narain ◽  
Naoki Sasakura ◽  
Yuki Sato
Keyword(s):  
Tensor Model ◽  
Tensor Networks ◽  
Random Tensor

scholarly journals Ryu-Takayanagi formula for symmetric random tensor networks

2018 ◽  
Vol 97 (12) ◽  
Author(s):  
Goffredo Chirco ◽  
Daniele Oriti ◽  
Mingyi Zhang
Keyword(s):  
Tensor Networks ◽  
Random Tensor

scholarly journals Entanglement transitions from holographic random tensor networks

2019 ◽  
Vol 100 (13) ◽  
Author(s):  
Romain Vasseur ◽  
Andrew C. Potter ◽  
Yi-Zhuang You ◽  
Andreas W. W. Ludwig
Keyword(s):  
Tensor Networks ◽  
Random Tensor

scholarly journals Holographic Entanglement in Group Field Theory

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 211 ◽  
Author(s):  
Goffredo Chirco
Keyword(s):  
Field Theory ◽  
Entanglement Entropy ◽  
Bipartite Network ◽  
Spin Network ◽  
Network State ◽  
Tensor Networks ◽  
Holographic Entanglement Entropy ◽  
Group Field Theory ◽  
Network States ◽  
Random Tensor

This work is meant as a review summary of a series of recent results concerning the derivation of a holographic entanglement entropy formula for generic open spin network states in the group field theory (GFT) approach to quantum gravity. The statistical group-field computation of the Rényi entropy for a bipartite network state for a simple interacting GFT is reviewed, within a recently proposed dictionary between group field theories and random tensor networks, and with an emphasis on the problem of a consistent characterisation of the entanglement entropy in the GFT second quantisation formalism.

scholarly journals Holographic coherent states from random tensor networks

2017 ◽  
Vol 2017 (8) ◽  
Author(s):  
Xiao-Liang Qi ◽  
Zhao Yang ◽  
Yi-Zhuang You
Keyword(s):  
Coherent States ◽  
Tensor Networks ◽  
Random Tensor

scholarly journals Asymptotic Expansion of the Multi-Orientable Random Tensor Model

10.37236/4629 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Eric Fusy ◽  
Adrian Tanasa
Keyword(s):  
Asymptotic Expansion ◽  
Matrix Models ◽  
Three Dimensional ◽  
Natural Generalization ◽  
General Term ◽  
Tensor Model ◽  
Half Integer ◽  
Tensor Models ◽  
Random Tensor

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expanion in $N$, the size of the tensor, of a particular random tensor model, the multi-orientable tensor model. We perform their enumeration and we establish which are the dominant configurations of a given degree.

scholarly journals A random matrix model with non-pairwise contracted indices

2019 ◽  
Vol 2019 (7) ◽  
Author(s):  
Luca Lionni ◽  
Naoki Sasakura
Keyword(s):  
Matrix Model ◽  
Random Matrix ◽  
Spherical Model ◽  
Tensor Model ◽  
Probabilistic Interpretation ◽  
Random Matrix Model ◽  
The Matrix ◽  
Replicated Systems ◽  
Random Tensor

Abstract We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the $p$-spin spherical model for the spin glass. We analyze the model using Feynman diagrammatic expansions, and provide an exhaustive characterization of the graphs that dominate when the dimensions of the pairwise and (or) non-pairwise contracted indices are large. We apply this to investigate the properties of the wave function of a toy model closely related to a tensor model in the Hamilton formalism, which is studied in a quantum gravity context, and obtain a result in favor of the consistency of the quantum probabilistic interpretation of this tensor model.

scholarly journals Petz reconstruction in random tensor networks

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hewei Frederic Jia ◽  
Mukund Rangamani
Keyword(s):  
Boundary Data ◽  
Coarse Graining ◽  
Random Projections ◽  
Replica Trick ◽  
Tensor Networks ◽  
Tensor Network ◽  
Random Tensor

Abstract We illustrate the ideas of bulk reconstruction in the context of random tensor network toy models of holography. Specifically, we demonstrate how the Petz reconstruction map works to obtain bulk operators from the boundary data by exploiting the replica trick. We also take the opportunity to comment on the differences between coarse-graining and random projections.

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