PIRSA:13080057 Scientific Series Condensed Matter

DOI10.48660/13080057

Series: Quantum Matter

White, S. (2013). Wavelets and MERA. Perimeter Institute. https://pirsa.org/13080057

White, Steven. Wavelets and MERA. Perimeter Institute, Aug. 30, 2013, https://pirsa.org/13080057 

@misc{ pirsa_PIRSA:13080057,
  doi = {10.48660/13080057},
  url = {https://pirsa.org/13080057},
  author = {White, Steven},
  keywords = {Condensed Matter},
  language = {en},
  title = {Wavelets and MERA},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {aug},
  note = {PIRSA:13080057 see, \url{https://pirsa.org}}
}

Abstract

Some of the key insights that led to the development of DMRG stemmed from studying the behavior of real space RG for single particle wavefunctions, a much simpler context than the many-particle case of main interest.  Similarly, one can gain insight into MERA by studying wavelets.  I will introduce basic wavelet theory and show how one of the most well-known wavelets, a low order orthogonal wavelet of Daubechies, can be realized as the fixed point of a specific MERA (in single-particle direct-sum space).  Higher order wavelets and the conflict between compactness in real and Fourier space may provide insight into generalized MERAs for many particle systems.

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