scholarly journals Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices

2016 ◽  
Vol 93 (12) ◽  
Author(s):  
Hui-Hai Zhao ◽  
Zhi-Yuan Xie ◽  
Tao Xiang ◽  
Masatoshi Imada
Keyword(s):  
Coarse Graining ◽  
Network Algorithm ◽  
Tensor Network

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.

scholarly journals A simple tensor network algorithm for two-dimensional steady states

2017 ◽  
Vol 8 (1) ◽  
Author(s):  
Augustine Kshetrimayum ◽  
Hendrik Weimer ◽  
Román Orús
Keyword(s):  
Steady States ◽  
Two Dimensional ◽  
Network Algorithm ◽  
Tensor Network

scholarly journals Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory

Universe ◽  
2020 ◽  
Vol 6 (7) ◽  
pp. 97 ◽  
Author(s):  
William J. Cunningham ◽  
Bianca Dittrich ◽  
Sebastian Steinhaus
Keyword(s):  
Gauge Theories ◽  
Lattice Gauge Theory ◽  
Coarse Graining ◽  
Two Dimensions ◽  
Direct Access ◽  
Continuous Group ◽  
Spin Network ◽  
Lattice Gauge ◽  
Tensor Network ◽  
Lattice Gauge Theories

Tensor network methods are powerful and efficient tools for studying the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods have been applied to lattice gauge theories, yet these theories remain a challenge in ( 2 + 1 ) dimensions. In this article, we present a new (decorated) tensor network algorithm, in which the tensors encode the lattice gauge amplitude expressed in the fusion basis. This has several advantages—firstly, the fusion basis does diagonalize operators measuring the magnetic fluxes and electric charges associated to a hierarchical set of regions. The algorithm allows therefore a direct access to these observables. Secondly the fusion basis is, as opposed to the previously employed spin network basis, stable under coarse-graining. Thirdly, due to the hierarchical structure of the fusion basis, the algorithm does implement predefined disentanglers. We apply this new algorithm to lattice gauge theories defined for the quantum group SU ( 2 ) k and identify a weak and a strong coupling phase for various levels k . As we increase the level k , the critical coupling g c decreases linearly, suggesting the absence of a deconfining phase for the continuous group SU ( 2 ) . Moreover, we illustrate the scaling behaviour of the Wilson loops in the two phases.

A NEURAL NETWORK ALGORITHM FOR DENSITY MEASUREMENT OF MULTIPHASE FLOW

2012 ◽  
Vol 24 (2) ◽  
pp. 89-103 ◽  
Author(s):  
Nabeel Al-Rawahi ◽  
Mahmoud Meribout ◽  
Ahmed Al-Naamany ◽  
Ali Al-Bimani ◽  
Adel Meribout
Keyword(s):  
Neural Network ◽  
Multiphase Flow ◽  
Density Measurement ◽  
Network Algorithm ◽  
Neural Network Algorithm
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