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Wick's theorem for matrix product states.

R Hübener1, A Mari2, J Eisert1

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.

Physical Review Letters
|August 29, 2014
PubMed
Summary
This summary is machine-generated.

Matrix product states (MPS) and their continuous analogues, crucial for low-entanglement quantum systems, are fully characterized by their two- and three-point functions. This finding aids in reconstructing quantum states from correlation measurements.

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Area of Science:

  • Quantum Many-Body Physics
  • Quantum Field Theory
  • Condensed Matter Physics

Background:

  • Matrix product states (MPS) and their continuous analogues are essential variational methods for describing quantum many-body systems and fields with limited entanglement.
  • These states form the foundation of the density-matrix renormalization group (DMRG) method and its continuous extensions.
  • Understanding correlations in such systems is key to characterizing their properties.

Purpose of the Study:

  • To demonstrate that N-point correlation functions in translation-invariant MPS are determined by two- and three-point functions.
  • To explore the implications of this characterization for understanding correlations in low-entanglement quantum states.
  • To introduce a novel method for reconstructing quantum states using correlation measurements.

Main Methods:

  • Analysis of N-point functions for arbitrary operators within discrete and continuous translation-invariant matrix product states.
  • Theoretical investigation of the relationship between higher-point and lower-point correlation functions.
  • Exploration of applications in reconstructing unknown quantum states.

Main Results:

  • Generically, N-point functions in translation-invariant MPS are completely determined by the corresponding two- and three-point functions.
  • This result simplifies the characterization of correlations in quantum states with low entanglement.
  • A new pathway for state reconstruction from correlation measurements is established.

Conclusions:

  • The relationship between correlation functions offers a powerful tool for analyzing and reconstructing quantum states.
  • This finding has direct applications in experimental settings, such as characterizing one-dimensional continuous cold atom systems.
  • The established correlation function relations may facilitate the development of perturbative approaches for interacting quantum theories.