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We connect discrete wavelet transforms and entanglement renormalization for quantum systems. This work provides the first analytic multiscale entanglement renormalization ansatz (MERA) for critical systems using Daubechies wavelets.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Computational physics

Background:

  • Entanglement renormalization is a powerful technique for studying quantum many-body systems.
  • Discrete wavelet transforms offer a versatile tool for analyzing functions and signals.
  • Understanding critical phenomena in quantum systems remains a key challenge.

Purpose of the Study:

  • To establish a precise connection between discrete wavelet transforms and entanglement renormalization.
  • To apply this connection to construct analytic multiscale entanglement renormalization ansatz (MERA) states for critical systems.
  • To demonstrate the utility of Daubechies wavelets in this context.

Main Methods:

  • Utilizing Daubechies wavelets to construct approximations of ground states.
  • Applying real-space renormalization group transformations.
  • Analyzing free particle systems and the critical Ising model.

Main Results:

  • A precise link between discrete wavelet transforms and entanglement renormalization is established.
  • Analytic multiscale entanglement renormalization ansatz (MERA) states are derived for critical systems.
  • Daubechies wavelets are shown to effectively build MERA approximations.

Conclusions:

  • Discrete wavelet transforms provide a novel and effective method for constructing MERA states.
  • This approach offers new insights into the structure of entanglement in critical quantum systems.
  • The findings pave the way for further applications in quantum many-body physics.