scholarly journals A constructive bulk-boundary correspondence using multi-scale symmetric tensor networks

2018 ◽  
Author(s):  
Nathan McMahon
Keyword(s):  
Symmetric Tensor ◽  
Multi Scale ◽  
Tensor Networks ◽  
Boundary Correspondence

Robust endocytoscopic image classification based on higher-order symmetric tensor analysis and multi-scale topological statistics

2020 ◽  
Vol 15 (12) ◽  
pp. 2049-2059
Author(s):  
Hayato Itoh ◽  
Yukitaka Nimura ◽  
Yuichi Mori ◽  
Masashi Misawa ◽  
Shin-Ei Kudo ◽  
...  
Keyword(s):  
Image Classification ◽  
Symmetric Tensor ◽  
Higher Order ◽  
Tensor Analysis ◽  
Multi Scale

scholarly journals Towards a dS/MERA correspondence

2017 ◽  
Vol 26 (13) ◽  
pp. 1750143 ◽  
Author(s):  
Raj Sinai Kunkolienkar ◽  
Kinjal Banerjee
Keyword(s):  
Degrees Of Freedom ◽  
Discrete Version ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Multi Scale ◽  
Penrose Diagram ◽  
Tensor Networks ◽  
Recent Advances ◽  
Horizon Entropy ◽  
The Future

Recent advances have suggested that spacetime itself emerges from the entanglement of the quantum degrees of freedom living on the boundary. In the case of the anti-de Sitter (AdS) spacetimes, a particular class of tensor networks has been shown to realize the same via Multi-Scale Entanglement Renormalization Ansatz (MERA). In this paper, we suggest a prescription for the dS/MERA correspondence and recover a discrete version of dS Penrose diagram by using the MERA on conformal theories identified with the future/past boundaries ([Formula: see text]) of the dS spacetime. In this case, as anticipated, time appears as the emergent direction. We comment on the possible interpretation that the dS cosmological horizon entropy involves entanglement with degrees of freedom across the cosmological horizon as well as the implications of our construction for cosmology.

scholarly journals Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Juraj Hasik ◽  
Didier Poilblanc ◽  
Federico Becca
Keyword(s):  
Automatic Differentiation ◽  
Symmetric Tensor ◽  
Extensive Study ◽  
Square Lattice ◽  
Antiferromagnetic Order ◽  
Heisenberg Antiferromagnet ◽  
Frustrated Magnetism ◽  
Magnetic Systems ◽  
Tensor Networks ◽  
Consistent Picture

The recent progress in the optimization of two-dimensional tensor networks [H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Phys. Rev. X 9, 031041 (2019)] based on automatic differentiation opened the way towards precise and fast optimization of such states and, in particular, infinite projected entangled-pair states (iPEPS) that constitute a generic-purpose Ansatz for lattice problems governed by local Hamiltonians. In this work, we perform an extensive study of a paradigmatic model of frustrated magnetism, the J_1-J_2J1−J2 Heisenberg antiferromagnet on the square lattice. By using advances in both optimization and subsequent data analysis, through finite correlation-length scaling, we report accurate estimations of the magnetization curve in the N'eel phase for J_2/J_1 \le 0.45J2/J1≤0.45. The unrestricted iPEPS simulations reveal an U(1)U(1) symmetric structure, which we identify and impose on tensors, resulting in a clean and consistent picture of antiferromagnetic order vanishing at the phase transition with a quantum paramagnet at J_2/J_1 \approx 0.46(1)J2/J1≈0.46(1). The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.

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