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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Published on: September 5, 2019

Entanglement renormalization in two spatial dimensions.

G Evenbly1, G Vidal

  • 1School of Mathematics and Physics, University of Queensland, Brisbane 4072, Australia.

Physical Review Letters
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

We developed a new entanglement renormalization method for large quantum systems. This approach significantly reduces computational costs, enabling analysis of infinite quantum critical systems.

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Area of Science:

  • Quantum physics
  • Computational physics
  • Condensed matter theory

Background:

  • Simulating large quantum lattice systems is computationally demanding.
  • Entanglement renormalization offers a promising approach for quantum many-body problems.

Purpose of the Study:

  • To propose and test a novel entanglement renormalization scheme for large 2D quantum lattice systems.
  • To enable efficient simulations of quantum systems, particularly at quantum critical points.

Main Methods:

  • Developed an entanglement renormalization scheme tailored for 2D quantum lattice systems.
  • Applied the scheme to study the 2D quantum Ising model on square lattices of varying sizes, including infinite systems.
  • Computed ground states, local observables, and two-point correlators.

Main Results:

  • Simulation cost scales logarithmically with lattice size in translationally invariant systems.
  • Simulation cost becomes independent of lattice size at quantum critical points, allowing analysis of infinite systems.
  • Accurate estimates for the critical magnetic field and critical exponent beta were obtained for the 2D quantum Ising model.
  • The energy gap was found to scale as 1/L at the critical point.

Conclusions:

  • The proposed entanglement renormalization scheme is effective for large 2D quantum systems.
  • The method provides significant computational advantages, especially for systems at quantum criticality.
  • This work facilitates the study of complex quantum phenomena in large-scale systems.