Random tensor network states & Holography

par Cécilia Lancien (Institut Fourier)

mercredi 9 nov. 2022, 14:00 → 15:00 Europe/Paris

https://greenlight.virtualdata.cloud.math.cnrs.fr/b/fab-49u-gkt

Holographic models of quantum gravity conjecture a duality between the geometry of a bulk gravitational theory and the entanglement properties of a boundary conformal field theory. Tensor networks provide discrete toy-models for such correspondence, which appear to successfully reproduce several of the conjectured formulas. In particular, boundary states constructed from a bulk tensor network satisfy by construction an area law of entanglement, which is the primary expected feature of holographic states. In this talk, I will explain how picking the tensors composing the network at random provides a mathematically tractable model. Indeed, when doing so, the asymptotic spectral distribution of the corresponding random boundary states can be precisely characterized, and hence their asymptotic entanglement entropy as well. The latter turns out to be, as wanted, proportional to the area of the minimal surface inside the bulk enclosing the boundary subregion (rather than to its volume), with a correction term that depends on the number of such minimal surfaces. I will show how results of this kind can be obtained using tools from random matrix theory and free probability.
Based on joint work with Newton Cheng, Geoff Penington, Michael Walter and Freek Witteveen, available at arXiv:2206.10482.