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

TL;DR

This paper investigates how the transition from hyperbolic to Euclidean lattices affects boundary correlations and bulk density of states in tight-binding models, revealing robustness of boundary features despite bulk changes.

Contribution

It demonstrates that boundary physics related to hyperbolic lattices remains stable even with Euclidean defects, enabling easier experimental and numerical studies.

Findings

Bulk properties are significantly altered by Euclidean defects.

Boundary correlation functions are robust against high defect fractions.

Essential boundary physics can be preserved without perfect hyperbolic lattices.

Abstract

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 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.