Encoding the lattice in the Holography

One of the most wanted features of holography in its condensed matter physics application is to encode the structure of lattice, which is the most direct data of the material. In this paper, we propose a method to encode the lattice structure by embedding the tight binding data into the Dirac equation in the AdS bulk. We explicitly worked out the idea for the Graphene and Haldane model, and the result shows that some degrees of freedom escape the free-electron on-shell curve, and Green's function loses the pole structure completely. It implies that the electronic structure is not described by the band structure only, which is consistent with what many ARPES data tell us, and it also implies that the system is in non-fermi liquid even for the graphene, which is consistent with recent experiments for the clean graphene.