Matrix product states and projected entangled pair states

Autor(en)

J. Ignacio Cirac, David Pérez-García, Norbert Schuch, Frank Verstraete

Abstrakt

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.

Organisation(en)

Institut für Mathematik, Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Max-Planck-Institut für Quantenoptik, Munich Center for Quantum Science and Technology (MCQST), Universidad Complutense De Madrid, Instituto de Ciencias Matemáticas, Ghent University

Journal

Reviews of Modern Physics

Band

93

Anzahl der Seiten

65

ISSN

0034-6861

DOI

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

Publikationsdatum

12-2021

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik, 103012 Hochenergiephysik, 103029 Statistische Physik

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/4d2848a7-350b-45a6-a1f2-dda7396ca6cf