Projected Entangled Pair States

Autor(en)

G. Scarpa, A. Molnar, Y. Ge, J. J. Garcia-Ripoll, N. Schuch, D. Perez-Garcia, S. Iblisdir

Abstrakt

Matrix product states and projected entangled pair states (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While matrix product states are comprehensively understood, in PEPS fundamental questions, relevant analytically as well as numerically, remain open, such as how to encode symmetries in full generality, or how to stabilize numerical methods using canonical forms. Here, we show that these key problems, as well as a number of related questions, are algorithmically undecidable, that is, they cannot be fully resolved in a systematic way. Our work thereby exposes fundamental limitations to a full and unbiased understanding of quantum many-body systems using PEPS.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation, Institut für Mathematik

Externe Organisation(en)

Universidad Complutense De Madrid, Universidad Politécnica de Madrid, Instituto de Ciencias Matemáticas, Max-Planck-Institut für Quantenoptik, Munich Center for Quantum Science and Technology (MCQST), Spanish National Research Council (CSIC), Universitat de Barcelona

Journal

Physical Review Letters

Band

125

Seiten

210504-1 - 210504-6

Anzahl der Seiten

6

ISSN

0031-9007

DOI

https://doi.org/10.1103/PhysRevLett.125.210504

Publikationsdatum

11-2020

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik, 101028 Mathematische Modellierung

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/426e5c1e-53b7-4775-8101-8305d22c7a25