Conformal boundary as holographic dual to the hyperbolic fracton model

In addition to describing our universe, gravitational theories profoundly inspire the study of emergent properties of exotic phases of matter. While the anti-de Sitter/conformal field theory (AdS/CFT) correspondence is one of the most celebrated examples, the field of fractonic matter---driven in part by gapless phases resembling linearized gravity---has also seen rapid developments. Despite the deep implications of both areas, connections between them remain sparse, primarily due to the difficulty in constructing explicit models that encapsulate both fields' essential features. Here we demonstrate the efficacy of the recently proposed hyperbolic fracton model as a concrete model for AdS/CFT duality. Using explicit numerical and analytical calculations on the discrete hyperbolic lattice, we show that the boundary state exhibits conformal field theory properties. Our main result is that bulk defects induce an emergent temperature for the boundary state, proportional to the defect perimeter, in quantitative agreement with the expected behavior of a black hole in AdS spacetime. The hyperbolic fracton model thus emerges as a unique lattice model of holographic principle equipped with a well-defined bulk Hamiltonian and offers a promising gateway for studying a wide range of holographic phenomena.