In this paper we consider anisotropic S=1/2 antiferromagnets through a projected fermion description. The success of projected fermion methods for the isotropic system is reviewed. We present an analytical approximation to Gutzwiller approximation and illustrate it’s use by showing that it is consistent with the SU(2) symmetry of projected fermions. The anisotropic antiferromagnet is written in terms of a fermion mean field. We consider the case of Ising anisotropy and show that in the Ising limit a procedure of minimizing the post-projection energy of a fermion mean field state gives the correct Ising ground state.
A fermion-spin transformation is used to implement the charge-spin separation, and is developed to study the low-dimensional t-J model. In this approach, the charge and spin degrees of freedom of the physical electron are separated, and the charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is representd by a hard-core boson. The on-site local constraint for single occupancy is satisfied even in the mean-field approximation and the sum rule for the physical electron is obeyed. This approach can be applied to both one and two-dimensional systems. In the one-dimensional case, the spinon as well as the physical electron behave like Luttinger liquids. We have obtained a gapless charge and spin excitation spectrum, a good ground state energy, and a reasonable electron-momentum distribution within the mean-field approximation. The correct exponents of the correlation functions and momentum distribution are also obtained if the squeezing effect and rearrangement of the spin configurations are taken into account. In the two-dimensional case, within the mean-field approximation the magnetized flux state with a gap in the spinon spectrum has the lowest energy at half filling. The antiferromagnetic long-range order is destroyed by hole doping of the order \ensuremath{\sim}10-15 % for t/J=3-5 and a disordered flux state with gapless spinon spectrum becomes stable. The calculated specific heat is roughly consistent with observed results on copper oxide superconductors. The possible phase separation is also discussed at the mean-field level.
The effect of spin-charge separation on the kinetic energy (KE) of the two-dimensional $t\ensuremath{-}J$ model is examined. Using a sum rule, we derive an exact expression for the lowest possible KE
(Ebound) for any state without doubly occupied sites. The kinetic energies of the relevant slave-boson and Schwinger-boson mean-field (MF) states are found to be considerably larger than
Ebound. The MF states exhibit complete spin-charge separation, and form the basis of a number of microscopic theories. An examination of the momentum distribution reveals that the large increase in KE of the MF states is due to excessive depletion of electrons from the bottom of the band (Schwinger boson states) and holes from the top of the band (slave boson states). To see whether the excess KE is simply due to the poor treatment of the local constraints, we solve the constraint problem analytically for the Schwinger boson MF states in the
J=0 limit. This restores gauge invariance, incorrectly violated in the MF theories. The resulting state is a generalization of the Hartree-Fock state in the Hubbard model, but one that includes spin-wave excitations, removing a deficiency of the simple HF theory. Even after the constraints are imposed correctly, the MF kinetic energy is found to be much larger than
Ebound. These results support the notion, advanced in earlier papers, that spin-charge separation in the MF state costs excessive kinetic energy, and makes the state unstable toward recombination processes which lead to superconductivity in
d=2 and a Fermi liquid state in higher dimensions.
We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Neel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed.
A theoretical investigation of boson versions of the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}_{z}$ models on the square lattice is carried out, by means of Green's function Monte Carlo simulations. Accurate ground-state energy estimates as a function of hole doping are obtained, allowing one to investigate the stability of the uniform phase against separation of the system into hole-rich and hole-free phases. In the boson $t\ensuremath{-}{J}_{z}$ model, such a separation is found to occur for arbitrarily small values of
Jz, at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any
Jz>0. The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.