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Wick's theorem for matrix product states

  • Matrix product states and their continuous analogues are variational classes of states that capture quantum many-body systems or quantum fields with low entanglement; they are at the basis of the density-matrix renormalization group method and continuous variants thereof. In this work we show that, generically, N-point functions of arbitrary operators in discrete and continuous translation invariant matrix product states are completely characterized by the corresponding two- and three-point functions. Aside from having important consequences for the structure of correlations in quantum states with low entanglement, this result provides a new way of reconstructing unknown states from correlation measurements, e. g., for one-dimensional continuous systems of cold atoms. We argue that such a relation of correlation functions may help in devising perturbative approaches to interacting theories.

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Metadaten
Author:R. Huebener, Andrea Mari, Jens Eisert
DOI:https://doi.org/10.1103/PhysRevLett.110.040401
ISSN:0031-9007 (print)
Parent Title (English):Physical review letters
Publisher:American Physical Society
Place of publication:College Park
Document Type:Article
Language:English
Year of first Publication:2013
Year of Completion:2013
Release Date:2017/03/26
Volume:110
Issue:4
Pagenumber:5
Funder:EU (Qessence); EURYI; ERC; BMBF (QuOReP)
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert