Chapter

The ground state construction of the two-dimensional Hubbard model on the honeycomb lattice

Giuliani Alessandro

in Quantum Theory from Small to Large Scales

Published in print May 2012 | ISBN: 9780199652495
Published online September 2012 | e-ISBN: 9780191741203 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199652495.003.0010

Series: Lecture Notes of the Les Houches Summer School

The ground state construction of the two-dimensional Hubbard model on the honeycomb lattice

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The fermionic Hubbard model on the two-dimensional hexagonal lattice at half-filling is the simplest model for undoped single layer graphene with screened interactions. It is remarkable that, in the weak coupling regime, the ground state thermodynamic functions and the equilibrium correlations can be fully constructed (in the form of convergent resummed series in the coupling strength) by rigorous renormalization group methods. This chapter presents a self-contained proof of the analyticity of the specific ground state energy and it reviews the relevant multiscale cluster expansion methods, which are of growing importance in the condensed matter community and, in particular, in the study of interaction effects in graphene.

Keywords: graphene; Hubbard model; renormalization group; cluster expansion

Chapter.  39274 words.  Illustrated.

Subjects: Atomic, Molecular, and Optical Physics

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