P. W. Anderson, The Resonating Valence Bond State in La2CuO4 and Superconductivity, Science, vol.235, issue.4793, p.1196, 1987.
DOI : 10.1126/science.235.4793.1196

P. Hansmann, T. Ayral, L. Vaugier, P. Werner, and S. Biermann, and Dynamical Mean-Field Theory, Physical Review Letters, vol.110, issue.16, p.166401, 2013.
DOI : 10.1103/PhysRevLett.110.166401
URL : https://hal.archives-ouvertes.fr/cea-01342181

T. O. Wehling, E. ¸a¸s?o?¸a¸s?o?-glu, C. Friedrich, A. I. Lichtenstein, M. I. Katsnelson et al., Strength of Effective Coulomb Interactions in Graphene and Graphite, Physical Review Letters, vol.106, issue.23, p.236805, 2011.
DOI : 10.1103/PhysRevLett.106.236805

M. Schüler, M. Rösner, T. O. Wehling, A. I. Lichtenstein, and M. I. Katsnelson, Optimal Hubbard Models for Materials with Nonlocal Coulomb Interactions: Graphene, Silicene, and Benzene, Physical Review Letters, vol.111, issue.3, p.36601, 2013.
DOI : 10.1103/PhysRevLett.111.036601

A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Reviews of Modern Physics, vol.68, issue.1, p.13, 1996.
DOI : 10.1103/RevModPhys.68.13

G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet et al., Electronic structure calculations with dynamical mean-field theory, Reviews of Modern Physics, vol.78, issue.3, p.865, 2006.
DOI : 10.1103/RevModPhys.78.865

T. Maier, M. Jarrell, T. Pruschke, and M. H. Hettler, Quantum cluster theories, Reviews of Modern Physics, vol.77, issue.3, p.1027, 2005.
DOI : 10.1103/RevModPhys.77.1027

P. Werner, E. Gull, O. Parcollet, and A. J. Millis, Momentum-selective metal-insulator transition in the two-dimensional Hubbard model: An 8-site dynamical cluster approximation study, Physical Review B, vol.80, issue.4, p.45120, 2009.
DOI : 10.1103/PhysRevB.80.045120

M. Ferrero, P. S. Cornaglia, L. De-leo, O. Parcollet, G. Kotliar et al., Pseudogap opening and formation of Fermi arcs as an orbital-selective Mott transition in momentum space, Physical Review B, vol.80, issue.6, p.64501, 2009.
DOI : 10.1103/PhysRevB.80.064501

E. Gull, M. Ferrero, O. Parcollet, A. Georges, and A. J. Millis, Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model, Physical Review B, vol.82, issue.15, p.155101, 2010.
DOI : 10.1103/PhysRevB.82.155101

T. A. Maier, M. Jarrell, T. C. Schulthess, P. R. Kent, and J. B. White, -Wave Superconductivity in the 2D Repulsive Hubbard Model, Physical Review Letters, vol.95, issue.23, p.237001, 2005.
DOI : 10.1103/PhysRevLett.95.237001
URL : https://hal.archives-ouvertes.fr/in2p3-00758958

E. Gull, O. Parcollet, and A. J. Millis, Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model, Physical Review Letters, vol.110, issue.21, p.216405, 2013.
DOI : 10.1103/PhysRevLett.110.216405

H. Kusunose and J. , Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation, Journal of the Physical Society of Japan, vol.75, issue.5, p.54713, 2006.
DOI : 10.1143/JPSJ.75.054713

A. Toschi, A. A. Katanin, and K. Held, Dynamical vertex approximation: A step beyond dynamical mean-field theory, Physical Review B, vol.75, issue.4, p.45118, 2007.
DOI : 10.1103/PhysRevB.75.045118

G. Rohringer, A. Toschi, H. Hafermann, K. Held, V. I. Anisimov et al., One-particle irreducible functional approach: A route to diagrammatic extensions of the dynamical mean-field theory, Physical Review B, vol.88, issue.11, p.115112, 2013.
DOI : 10.1103/PhysRevB.88.115112

A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Dual fermion approach to nonlocal correlations in the Hubbard model, Physical Review B, vol.77, issue.3, p.33101, 2008.
DOI : 10.1103/PhysRevB.77.033101

A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein, and A. Georges, Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs, Physical Review B, vol.79, issue.4, p.45133, 2009.
DOI : 10.1103/PhysRevB.79.045133

C. J. Bolech, S. S. Kancharla, and G. Kotliar, Cellular dynamical mean-field theory for the one-dimensional extended Hubbard model, Physical Review B, vol.67, issue.7, p.75110, 2003.
DOI : 10.1103/PhysRevB.67.075110

A. I. Poteryaev, A. I. Lichtenstein, and G. Kotliar, Approach, Physical Review Letters, vol.93, issue.8, p.86401, 2004.
DOI : 10.1103/PhysRevLett.93.086401

N. Tong, Extended variational cluster approximation for correlated systems, Physical Review B, vol.72, issue.11, p.115104, 2005.
DOI : 10.1103/PhysRevB.72.115104

J. Merino, Nonlocal Coulomb Correlations in Metals Close to a Charge Order Insulator Transition, Physical Review Letters, vol.99, issue.3, p.36404, 2007.
DOI : 10.1103/PhysRevLett.99.036404

M. Aichhorn, H. G. Evertz, W. Der-linden, and M. Potthoff, Charge ordering in extended Hubbard models:???Variational cluster approach, Physical Review B, vol.70, issue.23, p.235107, 2004.
DOI : 10.1103/PhysRevB.70.235107

S. R. Hassan and L. De-'medici, Slave spins away from half filling: Cluster mean-field theory of the Hubbard and extended Hubbard models, Physical Review B, vol.81, issue.3, p.35106, 2010.
DOI : 10.1103/PhysRevB.81.035106

Q. Si and J. L. Smith, Kosterlitz-Thouless Transition and Short Range Spatial Correlations in an Extended Hubbard Model, Physical Review Letters, vol.77, issue.16, p.3391, 1996.
DOI : 10.1103/PhysRevLett.77.3391

R. Chitra and G. Kotliar, Effect of Long Range Coulomb Interactions on the Mott Transition, Physical Review Letters, vol.84, issue.16, p.3678, 2000.
DOI : 10.1103/PhysRevLett.84.3678

R. Chitra and G. Kotliar, Effective-action approach to strongly correlated fermion systems, Physical Review B, vol.63, issue.11, p.115110, 2001.
DOI : 10.1103/PhysRevB.63.115110

P. Sun and G. Kotliar, method, Physical Review B, vol.66, issue.8, p.85120, 2002.
DOI : 10.1103/PhysRevB.66.085120
URL : https://hal.archives-ouvertes.fr/hal-00371644

T. Ayral, P. Werner, and S. Biermann, and Dynamical Mean Field Theory, Physical Review Letters, vol.109, issue.22, p.226401, 2012.
DOI : 10.1103/PhysRevLett.109.226401
URL : https://hal.archives-ouvertes.fr/cea-01342181

T. Ayral, S. Biermann, and P. Werner, and dynamical mean field theory, Physical Review B, vol.87, issue.12, p.125149, 2013.
DOI : 10.1103/PhysRevB.87.125149
URL : https://hal.archives-ouvertes.fr/cea-01342181

A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Dual boson approach to collective excitations in correlated fermionic systems, Annals of Physics, vol.327, issue.5, p.1320, 2012.
DOI : 10.1016/j.aop.2012.01.002

E. G. Van-loon, H. Hafermann, A. I. Lichtenstein, A. N. Rubtsov, and M. I. Katsnelson, Plasmons in Strongly Correlated Systems: Spectral Weight Transfer and Renormalized Dispersion, Physical Review Letters, vol.113, issue.24, p.246407, 2014.
DOI : 10.1103/PhysRevLett.113.246407

H. Hafermann, E. G. Van-loon, M. I. Katsnelson, A. I. Lichtenstein, and O. Parcollet, Collective charge excitations of strongly correlated electrons, vertex corrections, and gauge invariance, Physical Review B, vol.90, issue.23, p.235105, 2014.
DOI : 10.1103/PhysRevB.90.235105
URL : https://hal.archives-ouvertes.fr/cea-01058821

H. Hafermann, Numerical Approaches to Spatial Correlations in Strongly Interacting Fermion Systems, 2010.

H. Hafermann, F. Lechermann, A. N. Rubtsov, M. I. Katsnelson, A. Georges et al., Strong Electronic Correlations: Dynamical Mean-Field Theory and Beyond, Modern Theories of Many-Particle Systems in Condensed Matter Physics, pp.145-214, 2012.
DOI : 10.1007/978-3-642-10449-7_4

H. Hafermann, G. Li, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein et al., Efficient Perturbation Theory for Quantum Lattice Models, Physical Review Letters, vol.102, issue.20, p.206401, 2009.
DOI : 10.1103/PhysRevLett.102.206401

P. Werner, A. Comanac, L. De-'medici, M. Troyer, and A. J. Millis, Continuous-Time Solver for Quantum Impurity Models, Physical Review Letters, vol.97, issue.7, p.76405, 2006.
DOI : 10.1103/PhysRevLett.97.076405

H. Hafermann, P. Werner, and E. Gull, Efficient implementation of the continuous-time hybridization expansion quantum impurity solver, Computer Physics Communications, vol.184, issue.4, p.1280, 2013.
DOI : 10.1016/j.cpc.2012.12.013

H. Hafermann, Self-energy and vertex functions from hybridization-expansion continuous-time quantum Monte Carlo for impurity models with retarded interaction, Physical Review B, vol.89, issue.23, p.235128, 2014.
DOI : 10.1103/PhysRevB.89.235128

L. Huang, T. Ayral, S. Biermann, and P. Werner, Extended dynamical mean-field study of the Hubbard model with long-range interactions, Physical Review B, vol.90, issue.19, p.195114, 2014.
DOI : 10.1103/PhysRevB.90.195114
URL : https://hal.archives-ouvertes.fr/cea-01342149

P. Werner and A. J. Millis, Dynamical Screening in Correlated Electron Materials, Physical Review Letters, vol.104, issue.14, p.146401, 2010.
DOI : 10.1103/PhysRevLett.104.146401

S. Brener, H. Hafermann, A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Dual fermion approach to susceptibility of correlated lattice fermions, Physical Review B, vol.77, issue.19, p.195105, 2008.
DOI : 10.1103/PhysRevB.77.195105

Y. Zhang and J. Callaway, Extended Hubbard model in two dimensions, Physical Review B, vol.39, issue.13, p.9397, 1989.
DOI : 10.1103/PhysRevB.39.9397

B. Davoudi and A. S. Tremblay, Non-perturbative treatment of charge and spin fluctuations in the two-dimensional extended Hubbard model: Extended two-particle self-consistent approach, Physical Review B, vol.76, issue.8, p.85115, 2007.
DOI : 10.1103/PhysRevB.76.085115

S. V. Vonsovsky and M. I. Katsnelson, C: Solid State Phys, J. Phys, vol.12, p.2043, 1979.

J. Otsuki, Spin-boson coupling in continuous-time quantum Monte Carlo, Physical Review B, vol.87, issue.12, p.125102, 2013.
DOI : 10.1103/PhysRevB.87.125102

G. Rohringer, A. Valli, and A. Toschi, Local electronic correlation at the two-particle level, Physical Review B, vol.86, issue.12, p.125114, 2012.
DOI : 10.1103/PhysRevB.86.125114

L. Brown, Quantum Field Theory, 1994.
DOI : 10.1017/CBO9780511622649