Information, Geometry, and Physics Seminar

The AdS/CFT correspondence is one of the deepest breakthroughs of the last decades in theoretical physics. A recently proposed way to get insights on various features of this duality is achieved by discretizing the Anti-de Sitter spacetime. Within this program, I consider the Poincaré disk and discretize it by introducing a regular hyperbolic tiling on it. The features of this discretization are expected to be identified in the quantum theory defined at the boundary of the hyperbolic tiling. In this talk, I discuss how a class of boundary Hamiltonians can be naturally obtained in this discrete geometry via an inflation rule that allows constructing the tiling using concentric layers of tiles. The models in this class are aperiodic spin chains. Using strong-disorder renormalization group (SDRG) techniques, I compute the mutual information of two disjoint intervals of these boundary theories and compare my results with the one in conformal field theory. Finally, to reproduce the entanglement structure of the boundary theory from a bulk perspective, I exploit the SDRG to construct a tensor network whose boundary state is the ground state of aperiodic spin chains.