11 S. Q. Shen. Phys. Rev. B 57 , 6474 (1998); H. Sakamoto, T. Momoi, and K. Kubo, Phys. Rev. B 65 , 224403 (2002); K. Sano and Y. Ono, J. Phys. Soc. Jpn. 72 , 1847 (2003); K. Sano and Y. Ono, J. Mag. Mag. Mat. 310 , e319 (2007); and references therein. See also T. Hotta, A. L. Malvezzi, and E. Dagotto, Phys. Rev. B 62 , 9432 (2000). 12 

M. Daghofer, A. Moreo, J. A. Riera, E. Arrigoni, D. J. Scalapino, and E. Dagotto, Phys. Rev. Lett. 101 , 237004 (2008). 13 

A. Moreo, M. Daghofer, J. A. Riera, and E. Dagotto, Phys. Rev. B 79 , 134502 (2009). 14 

See for example, E. Dagotto and T. M. Rice, Science 271 , 618 (1996) and references therein. 15 

E. Dagotto, J. Riera, D. Scalapino, Phys. Rev. B 45 , 5744 (1992); S. R. White, R. M. Noack and D. J. Scalapino, Phys. Rev. Lett. 73 , 886 (1994); R. M. Noack, S. R. White, and D. J. Scalapino, Phys. Rev. Lett. 73 , 882 (1994); S. White and D. Scalapino, Phys. Rev. Lett. 80 , 1272 (1998); G. B. Martins, C. Gazza, J. C. Xavier, A. Feiguin, and E. Dagotto Phys. Rev. Lett. 84 , 5844 (2000). 16 

J. C. Xavier, Phys. Rev. B 68 , 134422 (2003); J. C. Xavier, E. Miranda and E. Dagotto, Phys. Rev. B 70 , 172415 (2004). 17 

V. L. Ginzburg, Sov. Phys. JETP 4 , 153 (1957); N. F. Berk and J. R. Schrieffer, Phys. Rev. Lett. 17 , 433 (1966). 18 

D. Aoki, A. Huxley, E. Ressouche, D. Braithwaite, J. Flou- quet, J. P. Brison, E. Lhotel and C. Paulsen, Nature 413 , 613 (2001). 19 

C. Pfleider, M. Uhlarz, S. M. Hayden, R. Vollmer, H.v. Lohneysen, N. R. Bernhoeft, and C. G. Lonzarich, Nature 412 , 58 (2001). 20 

N. I. Karchev, K. B. Blagoev, K. S. Bedell, and P. B. Lit- 

tlewood, Phys. Rev. Lett. 86 , 846 (2001). 

21 R. Shen, Z. M. Zheng, and D. Y. Xing, Phys. Rev. Lett. 91 , 069702 (2003). 22 

Y. Zhou, J. Li, and Chang-De Gong, Phys. Rev. Lett. 91 , 069701 (2003). 23 

Y. N. Joglekar and A. H. MacDonald, Phys. Rev. Lett. 92 , 199705 (2004). 24 

S. Raghu, Xiao-Liang Qi, Chao-Xing Liu, D. J. Scalapino, and Shou-Cheng Zhang, Phys. Rev. B 77 , 220503(R) (2008). 25 

J. C. Slater and G. F. Koster, Phys. Rev. 94 , 1498 (1954). 26 

J. Kanamori, Prog. Theor. Phys. 30 , 275 (1963). 27 

H. Tang, J. Magn. Magn. Mater. 187 , 23 (1998). 28 

E. Dagotto, T. Hotta, and A. Moreo, Phys. Rep. 344 , 1 (2001). 29 

S. White, Phys. Rev. Lett. 69 , 2863 (1992). 30 

G. Alvarez, Comp. Phys. Comm. 180 , 1572 (2009). See also http://www.ornl.gov/˜gz1/dmrgPlusPlus/. 31 

C. de la Cruz, Q. Huang, J. W. Lynn, J. Li, W. Ratcliff II, J. L. Zarestky, H. A. Mook, G. F. Chen, J. L. Luo, N. L. Wang, Nature 453 , 899 (2008). 32 

Y. Wan and Q.-H. Wang, Europhys. Lett. 85 , 57007 (2009). 33 

Note that in the analytical discussion of the binding en- ergy, the plaquette-diagonal hopping amplitudes do not play a significant role. In fact, we also have found binding of electrons/holes for the cluster 2 × 4 at t 3 = t 4 = 0 and U eff < 0. 34 

C. Zener, Phys. Rev.B 81 , 440 (1951); C. Zener, Phys. Rev. B 82 , 403 (1951). 

