July 12, 2024
A tensor network approach to an AdS/QCFT correspondence": A talk held at "Tensor Networks: from Simulations to Holography III" (Perimeter Institute, November 16, 2020 - November 20, 2020). Abstract: AdS/CFT endows gravity in anti-de Sitter (AdS) spacetime with a dual description in certain conformal field theories (CFTs) with matching symmetries. Tensor networks on regular discretizations of AdS space provide natural toy models of AdS/CFT, but break the continuous bulk symmetries. In this talk, we discuss several aspects of such toy models based on tensor networks. We show that this produces a quasiregular conformal field theory (qCFT) on the boundary and rigorously compute its symmetries, entanglement properties, and central charge bounds, applicable to a wide range of existing models. An explicit AdS/qCFT model with exact fractional central charges is given by holographic quantum error correcting codes based on Majorana dimers. These models also realize the strong disorder renormalization group, resulting in new connections between critical condensed-matter models, exact quantum error correction, and holography. If time allows, we will briefly review other recent group research on using tensor network models in quantum many-body physics including many-body localization and time crystals as well as in probabilistic modelling. (Based on arXiv:2004.04173, Phys. Rev. A 102, 042407 (2020), Phys. Rev. Research 1, 033079 (2019), Science Advances 5, eaaw0092 (2019).)