A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a
T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-
Tc cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
Motion of a single hole is studied at finite temperatures in the t-J model on a slave-fermion Schwinger-boson representation. The spin fluctuation is treated with the mean-field theory of Arovas and Auerbach. The Green's function for the slave fermion is calculated within the self-consistent Born approximation. A sharp quasiparticle peak is found to be separated from a broad spectrum of incoherence in the spectral function for low temperatures. The Green's function for the physical hole is calculated by taking account of the multiple scattering between the slave fermion and the Schwinger boson. A bound state of the slave fermion and the Schwinger boson is found at low temperatures, suggesting that the spin and the charge cannot be separated into a simple form. The energy of the bound state is minimized at momenta (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2, \ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), indicating that a small pocketlike Fermi surface is formed around the momenta for low concentrations of dopant holes.
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.
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.
A microscopical theory of electron spectrum and superconductivity within the two-dimensional $t\ensuremath{-}J$ model in paramagnetic state is proposed. By employing the projection technique for the Green functions in terms of the Hubbard operators self-consistent Eliashberg equations are derived. A strong coupling of electrons with spin and charge fluctuations due to exchange and kinematical interactions is obtained. In the normal state, one-electron spectral functions reveal narrow quasiparticle peaks close to the Fermi surface (FS) with an additional broad incoherent band. The FS changes from holelike at low doping to electronlike for hole concentrations $\ensuremath{\delta}>0.3.$ In the superconducting state we observe d-wave pairing with the maximal ${T}_{c}\ensuremath{\simeq}0.04t$ at optimal doping $\ensuremath{\delta}\ensuremath{\simeq}0.3.$
The 2D t-J model is studied with exact-diagonalization techniques applied to clusters of sixteen to twenty sites with various hole doping levels. Already for two holes (\ensuremath{\ge}10% doping), a large electronic Fermi surface, compatible with Luttinger's theorem, is observed. The full single-particle Green's function is examined, and is shown to exhibit quasiparticlelike behavior, with dispersion consistent with the band structure of the noninteracting limit, and bandwidth scaling approximately as J for J smaller than t.