consistent with the exact result for the motion of one hole in an anti-ferromagnetic background, see, Y. Nagaoka, Phys. Rev. 147 , 392 (1966). 

[24] E. Manousakis, Rev. Mod. Phys. 66 , 763 (1994). 

[25] D.A. Huse, Phys. Rev. B 37 , 2380 (1988); K.J. Runge, Phys. Rev. B 45 , 12292 (1992); A. W. Sandvik, Phys.Rev. B 56 , 11678 (1997). 

[26] M. Yu Kagan and T.M. Rice, J. Phys.: Condens. Matter 6 , 3771 

(1994). 

[27] H.-Q. Zhou and J.P. Barjaktareviˇc, J. Phys. A: Math. Th eor. 41 412001 (2008); H.-Q. Zhou, J.-H. Zhao, and B. Li, J. Phys. A: Math. Theor. 41 492002 (2008); H.-Q. Zhou, R. Or´us, and G. Vidal, Phys. Rev. Lett. 100 , 080602 (2008). 

[28] H.-Q. Zhou, arXiv:0803.0585. 

[29] H.-Q. Zhou, arXiv:1001.3358. 

