FM 18-08; arXiv:0811.1881

Authors : Alessandro Giuliani, Vieri Mastropietro

Title: The 2D Hubbard model on the honeycomb lattice

Abstract: We consider the 2D Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state energy and we construct the correlation functions up to zero temperature in terms of convergent series; analiticity is proved by making use of constructive fermionic renormalization group methods. We show that the interaction produces a modification of the Fermi velocity and of the wave function renormalization without changing the asymptotic infrared properties of the model with respect to the unperturbed non-interacting case; this rules out the possibility of superconducting or magnetic instabilities in the ground state. We also prove that the correlations are asymptotically Lorentz invariant and that the hidden $U(1)$ Lorentz symmetry implies the validity of a Ward Identity.

Keywords: Graphene, 2D Hubbard model, Dirac points, degenerate Fermi surface, renormalization group, zero temperature correlations, effective QED.

Alessandro Giuliani,
Dipartimento di Matematica,
Universita' di Roma Tre,
L.go S. Leonardo Murialdo 1, 00146 Roma, Italy

Vieri Mastropietro,
Dipartimento di Matematica,
Universita' di Roma Tor Vergata,
Viale della ricerca Scientifica, 00133 Roma, Italia