PIRSA:22100081

Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings

Di Giulio, G. (2022). Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings. Perimeter Institute. https://pirsa.org/22100081

Di Giulio, Giuseppe. Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings. Perimeter Institute, Oct. 11, 2022, https://pirsa.org/22100081 

          @misc{ pirsa_PIRSA:22100081,
            doi = {10.48660/22100081},
            url = {https://pirsa.org/22100081},
            author = {Di Giulio, Giuseppe},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {oct},
            note = {PIRSA:22100081 see, \url{https://pirsa.org}}
          }

Giuseppe Di Giulio

University of Würzburg

Talk number
PIRSA:22100081
Collection
Talk Type
Subject
Abstract

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.

Zoom link:  https://pitp.zoom.us/j/95849965965?pwd=eEx5Q0gxR2orR0dzS2pQbG8rR09oUT09