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Entanglement renormalization.

G Vidal1

  • 1School of Physical Sciences, the University of Queensland, QLD 4072, Australia.

Physical Review Letters
|February 1, 2008
PubMed
Summary
This summary is machine-generated.

We developed a real-space renormalization group (RG) transformation for quantum systems. This method efficiently simulates large quantum spin systems, revealing layered entanglement structures at quantum critical points.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Computational physics

Background:

  • Simulating large quantum systems is computationally challenging.
  • Understanding ground state entanglement is crucial for characterizing quantum phases.
  • Renormalization group (RG) methods are powerful tools for studying critical phenomena.

Purpose of the Study:

  • To introduce a novel real-space renormalization group (RG) transformation for quantum systems.
  • To develop a computationally efficient method for simulating large quantum spin lattices.
  • To investigate the structure of ground state entanglement in quantum systems, particularly at criticality.

Main Methods:

  • A real-space RG transformation is proposed that partially disentangles and coarse-grains blocks of lattice sites.

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  • Numerical simulations are performed on the ground state of a 1D lattice at criticality.
  • The computational scaling of the RG transformation is analyzed, focusing on Hilbert space dimension requirements.

    • Main Results:

    • The coarse-grained sites require a Hilbert space dimension that remains constant with successive RG transformations.
    • This RG approach enables quasi-exact simulations of tens of thousands of quantum spins with logarithmic computational scaling.
    • Ground state entanglement in extended quantum systems is found to be organized in layers corresponding to different length scales.

    Conclusions:

    • The developed RG transformation offers a computationally efficient pathway to study large quantum systems.
    • Entanglement at quantum critical points exhibits a layered structure, with each length scale contributing equally.
    • This method provides new insights into the nature of entanglement and criticality in quantum many-body systems.