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The Two-Dimensional Hubbard Model on the Honeycomb Lattice

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Abstract

We consider the two-dimensional (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; analyticity 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 thermal ground state.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma Tre, L.go S. Leonardo Murialdo 1, 00146, Roma, Italy

    Alessandro Giuliani

  2. Dipartimento di Matematica, Università di Roma Tor Vergata, V.le della Ricerca Scientifica, 00133, Roma, Italy

    Vieri Mastropietro

Authors
  1. Alessandro Giuliani
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  2. Vieri Mastropietro
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Correspondence to Alessandro Giuliani.

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Communicated by M. Salmhofer

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Giuliani, A., Mastropietro, V. The Two-Dimensional Hubbard Model on the Honeycomb Lattice. Commun. Math. Phys. 293, 301–346 (2010). https://doi.org/10.1007/s00220-009-0910-5

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  • DOI: https://doi.org/10.1007/s00220-009-0910-5

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