ar X iv : c on d - m at / 9 50 60 70 v 1 1 5 Ju n 19 95 Marshall sign and the doped t − J model

Marshall sign and the doped t − J model Abstract Marshall sign as a sole source of sign problem hidden in an antiferromagnet is explored under doping. By tracking the Marshall sign, a zero spectral weight Z is revealed in the doped antiferromagnetic system. Z = 0 is caused by a phase string induced by the " bare " hole. By eliminating such a phase string through nonlocal transformations, a non-perturbative scheme is obtained. It is argued that this formalism provides a unique way to get access to the real ground state of the doped t − J model for both one-and two-dimensions. 1 According to Marshall, 1 the ground-state wavefunction of the Heisenberg Hamiltonian for a bipartite lattice is real and satisfies a sign rule. This sign rule can be uniquely determined by requiring that a flip of any two antiparallel spins at nearest-neighboring sites always involves a sign change in the wave function: ↑↓→ (−1) ↓↑. Such a Marshall sign has played a crucial role in the success of two types of approximate approaches: the resonant-valence-bond (RVB)-type variational wavefunction 2 proposed by Liang, Doucot and Anderson, which gives one of the lowest energy bound (-0.3344 J/per bond), and the Schwinger-boson mean-field state 3 where the Marshall sign is incorporated in the order parameter < σ σ ¯ b iσ ¯ b j−σ > (i and j are the nearest-neighboring sites). Difficulty arises when one tries to dope holes into this antiferromagnet. Doped holes are expected to mess up with the Marshall sign, and the latter becomes a crucial source of sign problem hidden in the spin background. Doping effect is described by the well-known t − J model as follows