SMuK 2023 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: AdS/CFT Correspondence and Hydrodynamic Transport

MP 9.4: Vortrag

Donnerstag, 23. März 2023, 12:10–12:30, ZEU/0250

Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings — Pablo Basteiro, Rathindra Nath Das, •Giuseppe Di Giulio, Johanna Erdmenger, Jonathan Karl, René Meyer, and Zhuo-Yu Xian — Julius-Maximilians-Universität Würzburg

The AdS/CFT correspondence is one of the most important 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, we consider the Poincaré disk and we discretize it by introducing a regular hyperbolic tiling on it. The features of this discretization are expected to be identified in the quantum theory living on the boundary of the hyperbolic tiling. In this talk, we 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 techniques, we study the entanglement entropy of these boundary theories, identifying a logarithmic growth in the subsystem size, with a coefficient depending on the bulk discretization parameters.