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Cirac, J. Ignacio and Pérez García, David and Schuch, Norbert and Verstraete, F.
(2021)
*Matrix product states and projected entangled pair states:
Concepts, symmetries, theorems.*
Reviews of modern physics, 93
.
045003.
ISSN 0034-6861

PDF
2MB |

Official URL: https://doi.org/10.1103/RevModPhys.93.045003

## Abstract

The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many-body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. How matrix product states and projected entangled pair states describe many-body wave functions in terms of local tensors is reviewed. These tensors express how the entanglement is routed, act as a novel type of nonlocal order parameter, and the manner in which their symmetries are reflections of the global entanglement patterns in the full system is described. The manner in which tensor networks enable the construction of real-space renormalization group flows and fixed points is discussed, and the entanglement structure of states exhibiting topological quantum order is examined. Finally, a summary of the mathematical results of matrix product states and projected entangled pair states, highlighting the fundamental theorem of matrix product vectors and its applications, is provided.

Item Type: | Article |
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Uncontrolled Keywords: | Matrix product states; Projected entangled pair states; Tensor network methods |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 75930 |

Deposited On: | 14 Dec 2022 08:34 |

Last Modified: | 14 Dec 2022 11:38 |

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