Toward random tensor networks and holographic codes in CFT
- URL: http://arxiv.org/abs/2302.02446v1
- Date: Sun, 5 Feb 2023 18:16:02 GMT
- Title: Toward random tensor networks and holographic codes in CFT
- Authors: Jeevan Chandra and Thomas Hartman
- Abstract summary: In spherically symmetric states in any dimension and more general states in 2d CFT, this leads to a holographic error-correcting code.
The code is shown to be isometric for light operators outside the horizon, and non-isometric inside.
The transition at the horizon occurs due to a subtle breakdown of the Virasoro identity block approximation in states with a complex interior.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In holographic CFTs satisfying eigenstate thermalization, there is a regime
where the operator product expansion can be approximated by a random tensor
network. The geometry of the tensor network corresponds to a spatial slice in
the holographic dual, with the tensors discretizing the radial direction. In
spherically symmetric states in any dimension and more general states in 2d
CFT, this leads to a holographic error-correcting code, defined in terms of OPE
data, that can be systematically corrected beyond the random tensor
approximation. The code is shown to be isometric for light operators outside
the horizon, and non-isometric inside, as expected from general arguments about
bulk reconstruction. The transition at the horizon occurs due to a subtle
breakdown of the Virasoro identity block approximation in states with a complex
interior.
Related papers
- Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries [0.0]
We investigate the topological-to-non-topological quantum phase transitions (QPTs) occurring in the Kitaev code under local perturbations.
Our results indicate a higher robustness of the topological phase of the Kitaev code against local perturbations if the boundary is made open along one direction.
arXiv Detail & Related papers (2024-05-01T09:52:39Z) - Holographic Codes from Hyperinvariant Tensor Networks [70.31754291849292]
We show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions.
This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states.
arXiv Detail & Related papers (2023-04-05T20:28:04Z) - Holographic properties of superposed quantum geometries [0.0]
We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data.
This class includes spin networks, the kinematic states of lattice gauge theory and discrete quantum gravity.
arXiv Detail & Related papers (2022-07-15T17:37:47Z) - Entanglement Renormalization of a $T\bar{T}$-deformed CFT [0.0]
We find a Gaussian approximation to the ground state of a $TbarT$-deformed scalar CFT on the line.
We discuss the non-localities induced by the $TbarT$-deformation at short length scales.
arXiv Detail & Related papers (2022-03-01T09:50:31Z) - Simulating thermal density operators with cluster expansions and tensor
networks [0.0]
We benchmark this cluster tensor network operator (cluster TNO) for one-dimensional systems.
We use this formalism for representing the thermal density operator of a two-dimensional quantum spin system at a certain temperature as a single cluster TNO.
We find through a scaling analysis that the cluster-TNO approximation gives rise to a continuous phase transition in the correct universality class.
arXiv Detail & Related papers (2021-12-02T18:56:44Z) - Boundary theories of critical matchgate tensor networks [59.433172590351234]
Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices.
For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states.
We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
arXiv Detail & Related papers (2021-10-06T18:00:03Z) - Manifold Learning via Manifold Deflation [105.7418091051558]
dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data.
Many popular methods can fail dramatically, even on simple two-dimensional Manifolds.
This paper presents an embedding method for a novel, incremental tangent space estimator that incorporates global structure as coordinates.
Empirically, we show our algorithm recovers novel and interesting embeddings on real-world and synthetic datasets.
arXiv Detail & Related papers (2020-07-07T10:04:28Z) - Tensor network models of AdS/qCFT [69.6561021616688]
We introduce the notion of a quasiperiodic conformal field theory (qCFT)
We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
arXiv Detail & Related papers (2020-04-08T18:00:05Z) - Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric
graphs [81.12344211998635]
A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs)
We propose Gauge Equivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge equivariant kernels.
Our experiments validate the significantly improved expressivity of the proposed model over conventional GCNs and other methods.
arXiv Detail & Related papers (2020-03-11T17:21:15Z) - Understanding Graph Neural Networks with Generalized Geometric
Scattering Transforms [67.88675386638043]
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks.
We introduce windowed and non-windowed geometric scattering transforms for graphs based upon a very general class of asymmetric wavelets.
We show that these asymmetric graph scattering transforms have many of the same theoretical guarantees as their symmetric counterparts.
arXiv Detail & Related papers (2019-11-14T17:23:06Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.