PHYSICAL REVIEW B VOLUME 49, NUMBER 10 1 MARCH 1994-II Instability of the Nagaoka ferromagnetic state of the two-dimensional infinite-U Hubbard model Z. Song Chinese Center of Advanced Science Technology (World Laboratory), P. O. Box 8730, Beijing 100080, China and Department of Physics, Nankai University, Tianjin 300071, China (Received 10 May 1993; revised manuscript received 6 October 1993) A variational wave function with spin zero is presented for the infinite-U Hubbard model on a square lattice with the hole concentration 5=0. 5. We find that the Nagaoka ferromagnetic state is unstable for this case in the thermodynamic limit. Some discussion about this method for other hole concentrations is given. The Hubbard model with infinite interaction, which is the simplest model to treat strong correlations, has a Hamiltonian of the form an (1) in the following form H=H +H =yH + y H t' (2) H= tg(C, — C, +C, C, ), (i, j )cr (1) where 4 where C; =C, (1 — n; } and (i, j ) denotes nearest neighbors. This Hamiltonian represents restricted hop- ping in a space with no doubly occupied sites. One of the most interesting problems related to this model is the sta- bility of the Nagaoka state. ' Numerical results seem to indicate that the Nagaoka state may be unstable for any finite hole concentration. In addition, Shastry, Krishnamurthy, and Anderson prove rigorously that the fully aligned ferromagnetic state cannot be the ground state on the square lattice for 5 greater than 0. 49. In re- cent work, we have proposed a perturbation approach to study the ground-state properties of the two-dimensional infinite-U Hubbard model. Our results indicated that the Nagaoka state is unstable for 5=0. 5. In this paper, we present a variational wave function with spin zero, which has lower energy than that of the Nagaoka state. This provides an upper bound to the ground-state energy. Considering the infinite-U Hubbard model on an 1V XN lattice (N is even and N »1), we decompose the NXN lattice into , 'N 2 X2 cluste—rs, and rewrite the Hamiltoni- a, p denotes two nearest-neighboring clusters a and p (a, p=1, 2, . .. , —, 'N }, and C, , C; denote the creation and annihilation operators in the site i of cluster a H is the hopping term of cluster a and H ~ is the hopping term between clusters a and p. Based on the ground states and excited states of H on the 2X2 cluster a, one can construct the variational wave function. The variational wave function is , (IG &+glG &) 1+g X g ~g) ya, P (4) where g is a parameter. State ~g) is the ground state of H 1 4 0 0 + 0 0 0 + + + 0 0 — 0 + 0++~2- 0 0 -~2+ 0 — v2 0 + 0 + v'2 (E = 2V 2t ), and— 0 + + 0 0 + +0+0 0 0 0 lp(a, p) & = [q(g~(1, —, ')) I1b&(3, — —, ') &+qlg~(1, — —, ') & lpg(3, —, ') & +q l@~(3,—, ') & lib~(1, — —, ') &+q I@i(3, — —, ') & lp~(1, —, ') &+@2(1, —, ') & 11(~(3, — —, ') & + le(1, — —, ') &I+)(3, —, ') &+ I@((3, —, ') &182(1, — —, ') &+ lpga(3, — —, ') & lpg(1, —, ') & &, 0163-1829/94/49(10)/6723(3)/$06. 00 49 6723 1994 The American Physical Society