PIRSA:17040036 Conference Condensed Matter Quantum Fields and Strings Quantum Gravity Quantum Information

DOI10.48660/17040036

Conference/School: Tensor Networks for Quantum Field Theories II

Scholz, V. (2017). Analytic approaches to tensor networks for field theories. Perimeter Institute. https://pirsa.org/17040036

Scholz, Volkher. Analytic approaches to tensor networks for field theories. Perimeter Institute, Apr. 19, 2017, https://pirsa.org/17040036 

@misc{ pirsa_PIRSA:17040036,
  doi = {10.48660/17040036},
  url = {https://pirsa.org/17040036},
  author = {Scholz, Volkher},
  keywords = {Condensed Matter, Quantum Fields and Strings, Quantum Gravity, Quantum Information},
  language = {en},
  title = {Analytic approaches to tensor networks for field theories},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {apr},
  note = {PIRSA:17040036 see, \url{https://pirsa.org}}
}

Abstract

I will discuss analytic approaches to construct tensor network representations of quantum field theories, more specifically conformal field theories in 1+1 dimensions. A key insight is that we should understand how well the tensor network can reproduce the correlation functions of the quantum field theory. Based on this measure of closeness, I will present rigorous results allowing for explicit error bounds which show that both Matrix product states (MPS) as well as the multiscale renormalization Ansatz (MERA) do approximate conformal field theories. In particular, I will discuss the case of Wess-Zumino-Witten models. based on joint work with Robert Koenig (MPS), Brian Swingle and Michael Walter (MERA)

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