title: Wick's theorem for matrix product states.
abstract: 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.
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: R
authors.initials: R
authors.lastname: Hübener
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany and Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany and NEST, Scuola Normale Superiore and Istituto di Nanoscienze-CNR, 56126 Pisa, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Mari
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: J
authors.initials: J
authors.lastname: Eisert