A relaxation-function theory for the dynamic spin susceptibility in the $t\text{\ensuremath{-}}J$ model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperatures. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on ${\text{La}}_{2\ensuremath{-}\ensuremath{\delta}}{\text{Sr}}_{\ensuremath{\delta}}{\text{CuO}}_{4}$. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its $\ensuremath{\omega}/T$ scaling behavior are calculated in a reasonable agreement with experimental and ED data.
We consider the dynamic charge susceptibility and the charge density waves in strongly-correlated electronic systems within the two-dimensional t-J-V model. Using the equation of motion method for the relaxation functions in terms of the Hubbard operators, we calculate the static susceptibility and the spectrum of charge fluctuations as functions of doped hole concentrations and temperature. Charge density waves emerge for a sufficiently strong intersite Coulomb interaction. Calculation of the dynamic charge susceptibility reveals a strong damping of charge density waves for a small hole doping and propagating high-energy charge excitations at large doping.
We calculate the spin correlation function and the magnetic longitudinal and transverse susceptibilities of a two-dimensional antiferromagnet doped with a small concentration of holes, in the $t\text{\ensuremath{-}}J$ model. We find that the motion of holes generates spin fluctuations that add to the quantum fluctuations, the spin correlations decaying with the inverse of the spin distance, while increasing with doping as the critical hole concentration, where the long-range order disappears, is approached. Moreover, the longitudinal susceptibility becomes finite in the presence of doping due to the strong damping effects induced by the hole motion, while the transverse susceptibility is renormalized by softening effects. Both the longitudinal and transverse susceptibilities increase with doping, the former more significantly than the latter. Our results imply that doping destroys the long-range order while local antiferromagnetic spin correlations persist. This is consistent with experiments on doped copper oxide superconductors.
We consider the slave-fermion--Schwinger-boson decomposition of a t-J model for a two-dimensional antiferromagnet in which the next-nearest-neighbor hopping is taken into account by an explicit t' term. This technique is particularly suitable to describe systems with low hole density, as in the parent phases of high-
Tc superconducting (HTSC) materials, and we examine the experimental consequences of the model. Using mean-field states which admit finite spiral and off-diagonal order, we compute first the dynamic susceptibility \ensuremath{\chi}(q,\ensuremath{\omega}) from fluctuations in the boson (spin) degrees of freedom, and investigate a selected parameter regime for the model to seek features consistent with inelastic neutron scattering experiments on underdoped HTSC crystals. We find peaks in the scattered intensity at incommensurate wave vectors (\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2
k0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}) and (\ensuremath{\pi},\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2
k0), but within our approximation the q-integrated susceptibility as a function of frequency and temperature resembles that from spin-wave theory, which does not contain the scaling behavior over all values of \ensuremath{\omega}/T found experimentally. We show also the form of the nuclear magnetic resonance relaxation time ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$(T), which measures the zero-frequency limit of the susceptibility. The imaginary part of the physical electron Green function is a convolution of both fermionic (hole) and bosonic Green functions, and so incorporates the effect of spin dynamics on the charge motion. We calculate the photoemitted intensity, a direct experimental measurement of this quantity, focusing on its behavior near the hole pockets at (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) which characterize this type of model. The peak photocurrent occurs not at the hole Fermi surface, but at points separated from it by
k0 due to the boson incommensuration.
We discuss the motion of a hole generated in the Cu-O plane in high-temperature superconductors at half filling. The system is described by the t-J model. Special attention is paid to the influence of spin fluctuations in the ground state on the hole motion. It is shown that they reduce the bandwidth of the excitation energy as compared to the motion within the N\'eel ground state. The calculations are based on a cumulant approach to dynamical correlation functions introduced recently. This approach allows for a proper treatment of the strong electronic correlations which are incorporated in the model. It also guarantees that only spin fluctuations ``connected'' to the hole motion can contribute to the physical quantities.
We study the t-J and the Hubbard models at zero temperature using exact-diagonalization techniques on \ensuremath{\surd}10 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}10 and 4\ifmmode\times\else\texttimes\fi{}4 sites clusters. Quantum Monte Carlo simulation results on larger lattices are also presented. All electronic fillings have been analyzed for the three models. We have measured equal-time correlation functions corresponding to various types of order (ranging from ``standard'' staggered spin order to more ``exotic'' possibilities like chiral order), as well as various dynamical properties of these models. Upper bounds for the critical hole doping (
xc), where long-range antiferromagnetic order disappears, are presented. It was found that
xc is very small in agreement with experiments for the high-
Tc superconductors. For example, in the t-J model, ${\mathit{x}}_{\mathit{c}}$0.08 at J/t=0.4. However, short-distance spin correlations are important up to much higher dopings producing a sharp well-defined spin-wave-like peak in S(q=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega}). Regarding the possibility of phase separation in the Hubbard model, we have studied the behavior of the density of particles, 〈n〉, as a function of the chemical potential, using the Lanczos method on a 4\ifmmode\times\else\texttimes\fi{}4 Hubbard cluster, finding no indications of phase separation for any value of U/t. Then, we conclude that the t-J model at small J/t should not phase separate.In order to compare theoretical predictions with photoemission experiments, we evaluated the electronic density of states N(\ensuremath{\omega}), of the Hubbard and t-J models at several doping fractions. We found that upon doping the antiferromagnetic gap is filled for U\ensuremath{\sim}8t or smaller. The chemical potential moves across the insulating gap as one goes from electron to hole doping of the half-filled cluster, in agreement with x-ray absorption experiments but at variance with photoemission experiments. We have also calculated the optical conductivity, ${\mathrm{\ensuremath{\sigma}}}_{1}$(\ensuremath{\omega}), of the Hubbard and t-J models at all dopings on 4\ifmmode\times\else\texttimes\fi{}4 clusters. Results are compared with experiments and the weight of the Drude peak is presented as a function of couplings and dopings. Spectral weight found at small frequencies is associated with the mid-infrared band observed experimentally in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$
SrxCuO4, and with the states filling the insulating gap in photoemission experiments. An overall good agreement with experiments in the normal state was found. Regarding the possibility of superconductivity n these models, we have studied s-, d-, and p-wave pairing correlations. Naively, the d-wave channel seems enhanced near half filling while the extended s-wave channel seems enhanced from half filling up to 40% doping.However, we found that the enhancement comes from short-distance effects and, thus, no numerical indications of superconductivity were found in these models. We emphasize the importance of analyzing the pairing correlations as a function of distance to distinguish between short- and long-distance effects in the susceptibilities. We also observed that spiral order is enhanced at small J/t and low doping. Uniform chiral rder is suppressed by dynamical holes while staggered chiral order may be enhanced, although with a small plaquette order parameter. We conclude with the observation that the simple one-band Hubbard model with intermediate values of U\ensuremath{\sim}8t may account for many of the ``anomalous'' properties of the normal state of the high-
Tc superconductors.