Stability of the ferromagnetic state with respect to a single spin flip: Variational calculations for theU=∞ Hubbard model on the square lattice

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Abstract
We generalize a variational wave function for the U=∞ Hubbard model recently proposed by Shastry et al. [Phys. Rev. B 41, 2375 (1990)] to study the stability of the ferromagnetic state with respect to a single spin flip, and for the square lattice find an instability above a hole density δ=0.41. The form of our wave function is consistent with the picture suggested by Roth [J. Phys. Chem. Solids 28, 1549 (1967); Phys. Rev. 184, 451 (1969); 186, 428 (1969)] that the flipped spin binds an electron of opposite spin. We also obtain good upper bounds on the energy of spin-wave excitations for δet al.