Projected entangled pair states: fundamental analytical and numerical limitations

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Scarpa, G. and Molnár, Andras and Gé, Y. and García-Ripoll, J.J. and Schuch, N. and Pérez García, David and Iblisdir, S. (2020) Projected entangled pair states: fundamental analytical and numerical limitations. Physical Review Letters, 125 . p. 210504. ISSN 0031-9007

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Abstract

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 manybody systems using PEPS.


Item Type:Article
Uncontrolled Keywords:Quantum simulations; Computational complexity; Projected entangled pair states
Palabras clave (otros idiomas):Simulación cuántica; Complejidad computacional; PEPS
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:63716
Deposited On:22 Jan 2021 10:19
Last Modified:25 Jan 2021 09:06

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