R. Jördens, N. Strohmaier, K. Günter, H. Moritz, and T. Esslinger, A Mott insulator of fermionic atoms in an optical lattice, Nature, vol.90, issue.7210, p.204, 2008.
DOI : 10.1038/nature07244

W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden, V. et al., Functional renormalization group approach to correlated fermion systems, Reviews of Modern Physics, vol.84, issue.1, p.299, 2012.
DOI : 10.1103/RevModPhys.84.299

]. D. Sen12 and . Sénéchal, Strongly correlated systems, Springer Series in Solid-State Sciences 171, 2012.

W. Q. Yang, T. M. Chen, M. Rice, F. Sigrist, and . Zhang, model applied to the cuprate superconductors, New Journal of Physics, vol.11, issue.5, p.55053, 2009.
DOI : 10.1088/1367-2630/11/5/055053

H. Yokoyama, M. Ogata, Y. Tanaka, K. Kobayashi, and H. Tsuchiura, -Wave Pairing State in Two-Dimensional Hubbard Model, Journal of the Physical Society of Japan, vol.82, issue.1, p.14707, 2013.
DOI : 10.7566/JPSJ.82.014707

URL : https://hal.archives-ouvertes.fr/halshs-00309550

M. L. Medarde and J. Phys, Structural, magnetic and electronic properties of perovskites (R = rare earth), Journal of Physics: Condensed Matter, vol.9, issue.8, p.1679, 1997.
DOI : 10.1088/0953-8984/9/8/003

R. Von-helmolt, J. Wecker, B. Holzapfel, L. Schultz, K. Samwer et al., ferromagnetic films, Maignan, C. Simon, V. Caignaert, and B. Raveau, Solid State Commun, pp.2331-623, 1993.
DOI : 10.1103/PhysRevLett.71.2331

A. P. Malozemoff, J. Mannhart, and D. Scalapino, High-Temperature Cuprate Superconductors Get to Work, Physics Today, vol.58, issue.4, p.41, 2005.
DOI : 10.1063/1.1955478

J. G. Bednorz, K. A. Müller, B. Raveau, C. Michel, M. Hervieu et al., Crystal Chemistry of High-Tc Superconducting Copper Oxides, Z. Physik B Series in Material Science, vol.64, issue.15, 1986.

L. Li, C. Richter, S. Paetel, T. Kopp, J. Mannhart et al., Very Large Capacitance Enhancement in a Two-Dimensional Electron System, Science, vol.332, issue.6031, p.825, 2011.
DOI : 10.1126/science.1204168

S. Aasland, H. Fjellvag, B. C. Hauback, H. Kageyama, K. Yoshimura et al., Solid State Comm, Phys. Soc. Japan Eur. Phys. J. B, vol.101, issue.15, pp.1607-657, 1997.

U. Lüders, W. C. Sheets, A. David, W. Prellier, and R. Frésard, superlattices by geometrically confined doping, Physical Review B, vol.80, issue.24, p.241102, 2009.
DOI : 10.1103/PhysRevB.80.241102

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

W. Metzner and D. Vollhardt, Dimensions, Physical Review Letters, vol.62, issue.3, p.324, 1989.
DOI : 10.1103/PhysRevLett.62.324

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

F. F. Assaad and M. Imada, Insulator-Metal Transition in the One- and Two-Dimensional Hubbard Models, Physical Review Letters, vol.76, issue.17, p.3176, 1996.
DOI : 10.1103/PhysRevLett.76.3176

A. Avella and F. Mancini, Theoretical Methods for Strongly Correlated Systems, 2011.

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

URL : http://arxiv.org/abs/cond-mat/0404055

B. Edegger, V. N. Muthukumar, and C. Gros, Gutzwiller???RVB theory of high-temperature superconductivity: Results from renormalized mean-field theory and variational Monte Carlo calculations, Advances in Physics, vol.74, issue.6, p.927, 2007.
DOI : 10.1103/PhysRev.112.1900

M. Raczkowski, R. Frésard, and A. M. Ole´sole´s, Interplay between incommensurate phases in the cuprates, Europhysics Letters (EPL), vol.76, issue.1, p.128, 2006.
DOI : 10.1209/epl/i2006-10227-1

G. Seibold and J. Lorenzana, Stability of metallic stripes in the one-band extended Hubbard model, Physical Review B, vol.69, issue.13, p.134513, 2004.
DOI : 10.1103/PhysRevB.69.134513

S. R. White, D. J. Scalapino, R. L. Sugar, E. Y. Loh, J. E. Gubernatis et al., Numerical study of the two-dimensional Hubbard model, Physical Review B, vol.40, issue.1, p.506, 1989.
DOI : 10.1103/PhysRevB.40.506

E. Kozik, K. Van-houcke, E. Gull, L. Pollet, N. Prokof-'ev et al., Diagrammatic Monte Carlo for correlated fermions, EPL (Europhysics Letters), vol.90, issue.1, p.10004, 2010.
DOI : 10.1209/0295-5075/90/10004

E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer et al., Continuous-time Monte??Carlo methods for quantum impurity models, Reviews of Modern Physics, vol.83, issue.2, p.349, 2011.
DOI : 10.1103/RevModPhys.83.349

O. Juillet and R. Frésard, Exotic spin, charge and pairing correlations of the two-dimensional doped Hubbard model: A symmetry-entangled mean-field approach, Physical Review B, vol.87, issue.11, p.115136, 2013.
DOI : 10.1103/PhysRevB.87.115136

URL : https://hal.archives-ouvertes.fr/in2p3-00805497

E. H. Lieb, Two theorems on the Hubbard model, Physical Review Letters, vol.62, issue.10, p.1201, 1989.
DOI : 10.1103/PhysRevLett.62.1201

A. Moreo and E. Dagotto, Ground-state quantum numbers of the half-filled Hubbard model, Physical Review B, vol.41, issue.13, p.9488, 1990.
DOI : 10.1103/PhysRevB.41.9488

C. Noce and M. Cuoco, Exact-diagonalization method for correlated-electron models, Physical Review B, vol.54, issue.18, p.13047, 1996.
DOI : 10.1103/PhysRevB.54.13047

H. Yokohama, M. Ogata, Y. Tanaka, K. Kobayashi, H. Tsuchiura et al., -Wave Pairing State in Two-Dimensional Hubbard Model, Journal of the Physical Society of Japan, vol.82, issue.1, pp.14707-14740, 2013.
DOI : 10.7566/JPSJ.82.014707

D. Tahara and M. Imada, Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization, Journal of the Physical Society of Japan, vol.77, issue.11, p.114701, 2008.
DOI : 10.1143/JPSJ.77.114701

K. W. Schmid, T. Dahm, J. Margueron, and H. Müther, Symmetry-projected variational approach to the one-dimensional Hubbard model, Physical Review B, vol.72, issue.8, p.85116, 2005.
DOI : 10.1103/PhysRevB.72.085116

R. Rodríguez-guzmán, K. W. Schmid, C. A. Jiménez-hoyos, and G. E. Scuseria, Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model, Physical Review B, vol.85, issue.24, p.245130, 2012.
DOI : 10.1103/PhysRevB.85.245130

M. Hamermesh, Group Theory and its Applications to Physical Problems, American Journal of Physics, vol.30, issue.10, 1962.
DOI : 10.1119/1.1941790

]. F. Ass98 and . Assaad, High performance computing in science and engineering '98, 1998.

]. Bla85, G. Blaizot, and . Ripka, Quantum Theory of Finite Systems, 1985.

M. Guerrero, G. Ortiz, and J. E. Gubernatis, Correlated wave functions and the absence of long-range order in numerical studies of the Hubbard model, Physical Review B, vol.59, issue.3, p.1706, 1999.
DOI : 10.1103/PhysRevB.59.1706

M. Hamermesh, Group Theory and its Applications to Physical Problems, American Journal of Physics, vol.30, issue.10, 1964.
DOI : 10.1119/1.1941790

M. Honma, T. Mizusaki, and T. Otsuka, Nuclear Shell Model by the Quantum Monte Carlo Diagonalization Method, Physical Review Letters, vol.77, issue.16, p.3315, 1996.
DOI : 10.1103/PhysRevLett.77.3315

]. P. Rin80, P. Ring, and . Schuck, The Nuclear Many-Body Problem, 2003.

]. H. Shi14, C. A. Shi, R. Jiménez-hoyos, G. E. Rodríguez-guzmán, S. Scuseria et al., Symmetry-projected wave functions in quantum Monte Carlo calculations, Physical Review B, vol.89, issue.12, p.125129, 2014.
DOI : 10.1103/PhysRevB.89.125129

T. Yanagisawa, M. Miyazaki, and K. Yamagi, Correlated-Electron Systems and High-Temperature Superconductivity, Journal of Modern Physics, vol.04, issue.06, p.33, 2013.
DOI : 10.4236/jmp.2013.46A008

H. Yokohama, M. Ogata, Y. Tanaka, K. Kobayashi, and H. Tsuchiura, -Wave Pairing State in Two-Dimensional Hubbard Model, Journal of the Physical Society of Japan, vol.82, issue.1, p.14707, 2013.
DOI : 10.7566/JPSJ.82.014707

I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Reviews of Modern Physics, vol.80, issue.3, p.885, 2008.
DOI : 10.1103/RevModPhys.80.885

URL : https://hal.archives-ouvertes.fr/hal-00195515

M. W. Zwierlein, J. R. Abo-shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, Vortices and superfluidity in a strongly interacting Fermi gas, Nature, vol.435, issue.7045, p.1047, 2005.
DOI : 10.1038/nature03858

M. W. Zwierlein, C. H. Schunck, A. Schirotzek, and W. Ketterle, Direct observation of the superfluid phase transition in ultracold Fermi gases, Nature, vol.9, issue.7098, p.54, 2006.
DOI : 10.1038/nature04936

C. Sanner, E. J. Su, W. Huang, A. Keshet, J. Gillen et al., Correlations and Pair Formation in a Repulsively Interacting Fermi Gas, Physical Review Letters, vol.108, issue.24, p.240404, 2012.
DOI : 10.1103/PhysRevLett.108.240404

G. B. Jo, Y. R. Lee, J. H. Choi, C. A. Christensen, T. H. Kim et al., Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms, Science, vol.325, issue.5947, p.1521, 2009.
DOI : 10.1126/science.1177112

M. Lewenstein, A. Sampera, V. Ahufinger, B. Damski, A. Sen et al., Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond, Advances in Physics, vol.70, issue.2, p.243, 2007.
DOI : 10.1103/PhysRevLett.72.797

M. Köhl, H. Moritz, T. Stöferle, K. Günter, and T. Esslinger, Fermionic Atoms in a Three Dimensional Optical Lattice: Observing Fermi Surfaces, Dynamics, and Interactions, Physical Review Letters, vol.94, issue.8, p.80403, 2005.
DOI : 10.1103/PhysRevLett.94.080403

J. K. Chin, D. E. Miller, Y. Liu, C. Stan, W. Setiawan et al., Evidence for superfluidity of ultracold fermions in an optical lattice, Nature, vol.56, issue.7114, p.961, 2006.
DOI : 10.1038/nature05224

Y. L. Loh and N. Trivedi, Detecting the Elusive Larkin-Ovchinnikov Modulated Superfluid Phases for Imbalanced Fermi Gases in Optical Lattices, Physical Review Letters, vol.104, issue.16, p.165302, 2010.
DOI : 10.1103/PhysRevLett.104.165302

P. 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

E. Fradkin, S. A. Kivelson, and J. Tranquada, : Theory of intertwined orders in high temperature superconductors, Reviews of Modern Physics, vol.87, issue.2, p.457, 2015.
DOI : 10.1103/RevModPhys.87.457

E. H. Lieb and F. Wu, Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension, Physical Review Letters, vol.20, issue.25, p.1445, 1968.
DOI : 10.1103/PhysRevLett.20.1445

R. Bulla, T. Costi, and D. Vollhardt, Finite-temperature numerical renormalization group study of the Mott transition, Physical Review B, vol.64, issue.4, p.45103, 2001.
DOI : 10.1103/PhysRevB.64.045103

M. Troyer and U. Wiese, Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations, Physical Review Letters, vol.94, issue.17, p.170201, 2005.
DOI : 10.1103/PhysRevLett.94.170201

S. Liang and H. Pang, Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective, Physical Review B, vol.49, issue.13, p.9214, 1994.
DOI : 10.1103/PhysRevB.49.9214

Y. Deng, E. Kozik, N. Prokof-'ev, and S. , Emergent BCS regime of the two-dimensional fermionic Hubbard model: Ground-state phase diagram, EPL (Europhysics Letters), vol.110, issue.5, p.57001, 2015.
DOI : 10.1209/0295-5075/110/57001

R. Jördens, N. Strohmaier, K. Günter, H. Moritz, and E. , A Mott insulator of fermionic atoms in an optical lattice, Nature, vol.90, issue.7210, p.204, 2008.
DOI : 10.1038/nature07244

R. A. Hart, P. M. Duarte, T. L. Yang, X. Liu, T. Paiva et al., Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms, Nature, vol.106, issue.7542, p.211, 2015.
DOI : 10.1038/nature14223

K. Van-houcke, F. Werner, E. Kozik, N. Prokof-'ev, B. Svistunov et al., Feynman diagrams versus Fermi-gas Feynman??emulator, Nature Physics, vol.31, issue.5, p.366, 2012.
DOI : 10.1103/PhysRevLett.102.160401

URL : https://hal.archives-ouvertes.fr/hal-00721961

S. Nascimbène, Y. A. Chen, M. Atala, M. Aidelsburger, S. Trotzky et al., Experimental Realization of Plaquette Resonating Valence-Bond States with Ultracold Atoms in Optical Superlattices, Physical Review Letters, vol.108, issue.20, p.205301, 2012.
DOI : 10.1103/PhysRevLett.108.205301

C. J. Halboth and W. Metzner, Renormalization-group analysis of the two-dimensional Hubbard model, Physical Review B, vol.61, issue.11, p.7364, 2000.
DOI : 10.1103/PhysRevB.61.7364

W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden, and J. Schönhammer, Functional renormalization group approach to correlated fermion systems, Reviews of Modern Physics, vol.84, issue.1, p.299, 2012.
DOI : 10.1103/RevModPhys.84.299

D. Vollhardt, : an almost localized Fermi liquid, Reviews of Modern Physics, vol.56, issue.1, p.99, 1984.
DOI : 10.1103/RevModPhys.56.99

T. Giamarchi and C. Lhuillier, models by a variational Monte Carlo method, Physical Review B, vol.43, issue.16, p.12943, 1991.
DOI : 10.1103/PhysRevB.43.12943

M. Dzierzawa and R. Frésard, Gutzwiller wave-function approach to spiral magnetic order in the two-dimensional Hubbard model: A variational Monte Carlo study, Zeitschrift f???r Physik B Condensed Matter, vol.68, issue.2, p.245, 1993.
DOI : 10.1007/BF01315242

M. Miyazaki, K. Yamaji, T. Yanagisawa, and R. Kadono, Checkerboard States in the Two-Dimensional Hubbard Model with the Bi2212-Type Band, Journal of the Physical Society of Japan, vol.78, issue.4, p.43706, 2009.
DOI : 10.1143/JPSJ.78.043706

T. Misawa and M. Imada, superconductivity in doped Hubbard models and their extensions: Roles of uniform charge fluctuations, Physical Review B, vol.90, issue.11, p.115137, 2014.
DOI : 10.1103/PhysRevB.90.115137

C. C. Chang and S. Zhang, Spin and Charge Order in the Doped Hubbard Model: Long-Wavelength Collective Modes, Physical Review Letters, vol.104, issue.11, p.116402, 2010.
DOI : 10.1103/PhysRevLett.104.116402

O. Juillet and R. Frésard, Exotic spin, charge and pairing correlations of the two-dimensional doped Hubbard model: A symmetry-entangled mean-field approach, Physical Review B, vol.87, issue.11, p.115136, 2013.
DOI : 10.1103/PhysRevB.87.115136

URL : https://hal.archives-ouvertes.fr/in2p3-00805497

A. Leprévost, O. Juillet, and R. Frésard, Exact ground state of strongly correlated electron systems from symmetry-entangled wave-functions, Annalen der Physik, vol.85, issue.9-10, p.430, 2014.
DOI : 10.1002/andp.201400129

S. Bertsch, G. F. Robledo, and L. , Symmetry Restoration in Hartree-Fock-Bogoliubov Based Theories, Physical Review Letters, vol.108, issue.4, p.42505, 2012.
DOI : 10.1103/PhysRevLett.108.042505

J. F. Corney and P. Drummond, Gaussian Quantum Monte Carlo Methods for Fermions and Bosons, Physical Review Letters, vol.93, issue.26, p.260401, 2004.
DOI : 10.1103/PhysRevLett.93.260401

O. Juillet, Sign-free stochastic mean-field approach to strongly correlated phases of ultracold fermions, New Journal of Physics, vol.9, issue.6, p.163, 2007.
DOI : 10.1088/1367-2630/9/6/163

URL : https://hal.archives-ouvertes.fr/hal-00090944

T. Aimi and M. Imada, Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems, Journal of the Physical Society of Japan, vol.76, issue.8, p.84709, 2007.
DOI : 10.1143/JPSJ.76.084709

T. Aimi and M. Imada, Superconductivity in Copper Oxides?, Journal of the Physical Society of Japan, vol.76, issue.11, p.113708, 2007.
DOI : 10.1143/JPSJ.76.113708

H. Shi, C. A. Jimenez-hoyos, R. Rodriguez-guzman, G. E. Scuseria, and S. Zhang, Symmetry-projected wave functions in quantum Monte Carlo calculations, Physical Review B, vol.89, issue.12, p.125129, 2014.
DOI : 10.1103/PhysRevB.89.125129

D. Eichenberger and D. Baeriswyl, Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: A variational study, Physical Review B, vol.76, issue.18, p.180504, 2007.
DOI : 10.1103/PhysRevB.76.180504

P. Corboz, S. R. White, G. Vidal, and M. Troyer, model with infinite projected entangled-pair states, Physical Review B, vol.84, issue.4, p.41108, 2011.
DOI : 10.1103/PhysRevB.84.041108

P. Corboz, T. Rice, and M. Troyer, -Wave State versus Stripe State, Physical Review Letters, vol.113, issue.4, p.46402, 2014.
DOI : 10.1103/PhysRevLett.113.046402

URL : https://hal.archives-ouvertes.fr/hal-00694548

S. White and D. J. Scalapino, Ground states of the doped four-leg t-J ladder, Physical Review B, vol.55, issue.22, p.14701, 1997.
DOI : 10.1103/PhysRevB.55.R14701

S. R. White, I. Affleck, and D. J. Scalapino, Friedel oscillations and charge density waves in chains and ladders, Physical Review B, vol.65, issue.16, p.165122, 1997.
DOI : 10.1103/PhysRevB.65.165122

M. Raczkowski, R. Frésard, and A. Oles, Interplay between incommensurate phases in the cuprates, Europhysics Letters (EPL), vol.76, issue.1, p.128, 2006.
DOI : 10.1209/epl/i2006-10227-1

R. Peters and N. Kawakami, Spin density waves in the Hubbard model: A DMFT approach, Physical Review B, vol.89, issue.15, p.155134, 2014.
DOI : 10.1103/PhysRevB.89.155134

D. Bormann, T. Schneider, and M. Frick, Hubbard Model, Europhysics Letters (EPL), vol.14, issue.2, p.101, 1991.
DOI : 10.1209/0295-5075/14/2/002