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 talk 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.
Joint work with Andrea Mari and Jens Eisert.