PIRSA:13030117

Wick's theorem for Matrix Product states

Huebener, R. (2013). Wick's theorem for Matrix Product states. Perimeter Institute. https://pirsa.org/13030117

Huebener, Robert. Wick's theorem for Matrix Product states. Perimeter Institute, Mar. 25, 2013, https://pirsa.org/13030117 

          @misc{ pirsa_PIRSA:13030117,
            doi = {10.48660/13030117},
            url = {https://pirsa.org/13030117},
            author = {Huebener, Robert},
            keywords = {Quantum Information},
            language = {en},
            title = {Wick{\textquoteright}s theorem for Matrix Product states},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {mar},
            note = {PIRSA:13030117 see, \url{https://pirsa.org}}
          }

Robert Huebener Freie Universität Berlin

DOI 10.48660/13030117
Collection
Talk Type Scientific Series
Subject

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 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.
arXiv:1207.6537