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Quantum Theory from Small to Large ScalesLecture Notes of the Les Houches Summer School: Volume 95, August 2010$
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Jürg Frohlich, Manfred Salmhofer, Vieri Mastropietro, Wojciech De Roeck, and Leticia F. Cugliandolo

Print publication date: 2012

Print ISBN-13: 9780199652495

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780199652495.001.0001

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

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

Chapter:
(p.553) 10 The ground state construction of the two-dimensional Hubbard model on the honeycomb lattice
Source:
Quantum Theory from Small to Large Scales
Author(s):

Giuliani Alessandro

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199652495.003.0010

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

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