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**FM 2-2011 **(Ph.D. thesis, University of Rome "Sapienza")

**Author:** Marcello Porta

**Title:** *A lattice gauge theory model for graphene*

**Advisors:** *G. Gallavotti and V. Mastropietro*

**Abstract: **In this Ph.D. thesis a model for graphene in presence of quantized electromagnetic interactions is introduced. The zero and low temperature properties of the model are studied using rigorous renormalization group methods. In particular, it is shown that, at all orders in renormalized perturbation theory, the Schwinger functions and the response functions of the model decay with interaction dependent anomalous exponents. Regarding the 2-point Schwinger function, the wave function renormalization diverges in the infrared limit, while the effective Fermi velocity flows to the speed of light. Concerning the response functions, those associated to a KekulÃ© distortion of the honeycomb lattice and to a charge density wave instability are enhanced by the interaction (their scaling in real space is depressed), while the lowest order correction to the scaling exponent of the density-density response function is vanishing. Then, the model in presence of a fixed KekulÃ© distortion is studied, and it shown that the interaction provides a strong renormalization of the effective amplitude of the distortion. Finally, the possibility of spontaneous distortions of the lattice induced by strong enough electron-electron interactions is discussed.

**Keywords:** graphene, lattice gauge theories, Ward identities, anomalous exponents.

Marcello Porta

ETH - Institute for Theoretical Physics

Wolfgang Pauli Strasse 27, CH-8093

Zuerich - Switzerland

e-mail: mporta AT phys DOT ethz DOT ch