Bonn 2020 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 13: Tensor Networks

MP 13.2: Talk

Wednesday, April 1, 2020, 16:50–17:10, H-HS I

Scale and Translation invariant Tensor Networks — •Sukhbinder Singh — Max-Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam

Entanglement renormalization (ER) [1] is a lattice renormalization group (RG) transformation that is described by a tensor network. Substantial numerical evidence indicates that it is capable of approximating the expected RG fixed points, both in gapped and critical phases of 1D quantum lattice systems. ER also generates the multi-scale entanglement renormalization ansatz (MERA) [2] — an efficient tensor network representation, in particular, of 1D critical ground states, from which the underlying conformal field theory (CFT) data can be accurately estimated [3,4]. I will describe first steps towards formalizing the exact relationship between ER and RG fixed points (beyond numerical approximations). A generic ER transformation breaks the symmetries that emerge at RG fixed points. I will propose certain polynomial tensor constraints that characterize (a subset of) ER transformations with translation-invariant fixed points. I show that some solutions of these constraints correspond to 2d TQFTs, which describe RG fixed points in gapped phases. I discuss why there may also be solutions that correspond to 2d rational CFTs. An exact relationship between ER fixed points and 2d CFTs might provide a novel pathway to bootstrap 2d CFTs directly on the lattice and illuminate holographic properties of the MERA [5]. References 1. G. Vidal, PRL 99 (2007). 2. G. Vidal, PRL 101 (2008). 3. V. Giovannetti et al PRL. 101 (2008) 4. R. Pfeifer et al PRA(R) 79(4) (2009) 5. B. Swingle, PRD 86 (2012).