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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 2: Quantum Information and Gravity

MP 2.8: Vortrag

Montag, 18. März 2024, 12:40–13:00, HL 102

Critical models and discrete holography — •Dimitris Saraidaris and Alexander Jahn — Freie Universität Berlin, Germany

Tensor networks on hyperbolic lattices have been recently studied as prominent models of discrete holography. In particular, by filling the bulk of a hyperbolic lattice with matchgate tensors, following the inflation rules imposed by its geometry, the disordered states appearing on the boundary are related to critical models. We use the Multi-scale Quasicrystal Ansatz to translate these boundary states into coupling constants for the disordered XY and XXZ Heisenberg model with periodic boundary conditions. Firstly, we observe that there is a range of disorder strengths, that show entanglement entropy scaling similar to the uniform critical model. Generalizing to the non-Gaussian model, we observe that the criticality of the disordered boundary states does not depend on the choice of the tensors in the bulk, but on the geometry of the tiling. Finally, we study the same models with open boundary conditions. Here, we can find disordered models whose entanglement entropy exceeds the excepted value for the uniform critical model, with a correction term that grows linearly with subsystem size.

Keywords: Holography; Tensor Networks; Many body systems