Date : January 17, 2023, 16:00 CET

Johanna Erdmenger (University of W├╝rzburg)


Discrete Holography

Abstract: I will review recent progress towards establishing a holographic duality for discrete spaces involving a regular tiling of hyperbolic space. Discrete holography is of interest to a broad audience reaching – beyond holographers – from mathematicians interested in CFTs on fractals to condensed matter scientists and electrical engineers studying hyperbolic lattices. In the talk, I will present a recent example where an aperiodic XXZ spin chain is obtained naturally by extrapolating the bulk tiling to its boundary. The properties of this model are studied using RG techniques, which provide a tensor network construction for its ground state. We calculate and compare the entanglement entropy and mutual information both at the boundary and in the bulk. I will comment on the next steps towards obtaining a full dynamical duality of discrete systems.

Based on arXiv 2205.05693, 2205.05081 and 2212.11292