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arXiv · 1207.6537

Wick's theorem for matrix product states

R. Hübener·A. Mari·J. Eisert
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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 translationally 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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R. Hübener, A. Mari, J. Eisert. 2012-07-27. Wick's theorem for matrix product states. https://doi.org/10.1103/physrevlett.110.040401

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