Simulating holographic correspondence in flexible graphene

Abstract

In the spirit of the generalized holographic conjecture, we explore a relationship between the bulk and boundary properties of non-interacting massive Dirac fermions living on a flexible surface, such as a sheet of graphene. We demonstrate that the boundary correlations can mimic those normally found in the system of one-dimensional interacting fermions, a specific form of such phantom interaction being determined by the bulk geometry. This geometrical interpretation of the boundary interaction effects offers a new insight into the possible origin of the more sophisticated types of holographic correspondence and suggests potential ways of visualizing 'analogue holography' in the experimentally viable environments.