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00925njm 22002777a 4500 dc Scarpa, G. author Molnár, Andras author Gé, Y. author García Ripoll, J. J. author Schuch, N. author Pérez García, David author Iblisdir, Sofyan author 2020-11-20 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. Scarpa, G., Molnár, A., Gé, Y. et al. «Projected Entangled Pair States: Fundamental Analytical and Numerical Limitations». Physical Review Letters, vol. 125, n.o 21, noviembre de 2020, p. 210504. DOI.org (Crossref), https://doi.org/10.1103/PhysRevLett.125.210504. 0031-9007 10.1103/PhysRevLett.125.210504 https://hdl.handle.net/20.500.14352/7733 https//doi.org/10.1103/PhysRevLett.125.210504 http://prl.aps.org/ Projected entangled pair states: fundamental analytical and numerical limitations