Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices

We study tight-binding models in the crossover from hyperbolic to Euclidean lattices, realized through the successive insertion of Euclidean defects into hyperbolic lattices.

We analyze how the holographic two-point boundary correlation function and bulk density of states evolve as defects are gradually introduced.

We find that bulk properties are strongly affected by the presence of Euclidean defects, whereas boundary observables remain remarkably robust even at high defect fractions.

This robustness indicates that essential features of boundary physics on hyperbolic lattices, which capture aspects of anti de-Sitter/conformal field theory (AdS/CFT)-like dualities in discrete systems, can be reproduced both experimentally and numerically without requiring perfectly hyperbolic lattices, thereby reducing the system size needed for implementation.