scholarly journals Gapless Coulomb State Emerging from a Self-Dual Topological Tensor-Network State

2019 ◽  
Vol 122 (17) ◽  
Author(s):  
Guo-Yi Zhu ◽  
Guang-Ming Zhang
Keyword(s):  
Network State ◽  
Tensor Network ◽  
Topological Tensor

scholarly journals On the geometry of tensor network states

2012 ◽  
Vol 12 (3&4) ◽  
pp. 346-354
Author(s):  
Joseph M. Landsburg ◽  
Yang Qi ◽  
Ke Ye
Keyword(s):  
Graphical Models ◽  
Matrix Multiplication ◽  
Algebraic Statistics ◽  
Geometric Complexity ◽  
Network State ◽  
Geometric Complexity Theory ◽  
Tensor Networks ◽  
Tensor Network ◽  
Network States ◽  
Tensor Network States

We answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor networks states corresponding to trees and loops. Grasedyck's question has a surprising connection to the area of Geometric Complexity Theory, in that the result is equivalent to the statement that the boundary of the Mulmuley-Sohoni type variety associated to matrix multiplication is strictly larger than the projections of matrix multiplication (and re-expressions of matrix multiplication and its projections after changes of bases). Tensor Network States are also related to graphical models in algebraic statistics.

scholarly journals TNSPackage: A Fortran2003 library designed for tensor network state methods

2018 ◽  
Vol 228 ◽  
pp. 163-177 ◽  
Author(s):  
Shao-Jun Dong ◽  
Wen-Yuan Liu ◽  
Chao Wang ◽  
Yongjian Han ◽  
G.-C. Guo ◽  
...  
Keyword(s):  
Network State ◽  
Tensor Network

scholarly journals Algebraically contractible topological tensor network states

2011 ◽  
Vol 45 (1) ◽  
pp. 015309 ◽  
Author(s):  
S J Denny ◽  
J D Biamonte ◽  
D Jaksch ◽  
S R Clark
Keyword(s):  
Tensor Network ◽  
Network States ◽  
Tensor Network States ◽  
Topological Tensor

scholarly journals A hierarchy of topological tensor network states

2013 ◽  
Vol 54 (1) ◽  
pp. 012201 ◽  
Author(s):  
Oliver Buerschaper ◽  
Juan Martín Mombelli ◽  
Matthias Christandl ◽  
Miguel Aguado
Keyword(s):  
Tensor Network ◽  
Network States ◽  
Tensor Network States ◽  
Topological Tensor
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