On the geometry of tensor network states of 2 × N grids

Autor:	Parth Sarin
Rok vydání:	2019
Předmět:	Numerical Analysis Algebra and Number Theory 010102 general mathematics Geometry Torus 010103 numerical & computational mathematics Grid 01 natural sciences Graph Discrete Mathematics and Combinatorics Geometry and Topology Tensor 0101 mathematics Mathematics
Zdroj:	Linear Algebra and its Applications. 575:235-249
ISSN:	0024-3795
DOI:	10.1016/j.laa.2019.04.002
Popis:	We discuss the geometry of a class of tensor network states, called projected entangled pair states in the Physics literature. We provide initial results towards a question of Verstraete and Rizzi regarding the tensor network state of an M × N grid; we partially answer the question for a 2 × N grid. We also study the 2 × N grid sitting on a torus and provide initial results towards understanding the Zariski closure of the set of tensor network states associated to this graph. Finally, we give explicit tensors that provide optimal (using currently available methods) bounds on the border rank of a generic tensor in the tensor network state of the 2 × N grid.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a5d2e53a2019a7327c2e00b4a0112c34 https://doi.org/10.1016/j.laa.2019.04.002 Zobrazit plný text záznamu Full Text from ScienceDirect