We review recent results for the properties of doped antiferromagnets, obtained by the numerical analysis of the planar t-J model using the novel finite-temperature Lanczos method for small correlated systems. First we briefly summarize our present understanding of anomalous normal-state properties of cuprates, and present the electronic phase diagram, phenomenological scenarios and models proposed in this connection. The numerical method is then described in more detail. The following sections are devoted to various static and dynamical properties of the t-J model. Among the thermodynamic properties the chemical potential, entropy and the specific heat are evaluated. Discussing electrical properties the emphasis is on the planar optical conductivity and the d.c. resistivity. Magnetic properties involve the static and dynamical spin structure factor, as measured via the susceptibility measurements, the NMR relaxation and the neutron scattering, as well as the orbital current contribution. The analysis of electron spectral functions, studied by photoemission experiments, and their relation to the c-axis conductivity, follows. Finally we discuss density fluctuations, the electronic Raman scattering and the thermoelectric power. Whenever feasible a comparison with experimental data is performed. A general conclusion is that the t-J model captures well the main features of anomalous normal-state properties of cuprates, for a number of quantities the agreement is even a quantitative one. It is shown that several dynamical quantities exhibit at intermediate doping a novel universal behaviour consistent with a marginal Fermi-liquid concept, which seems to emerge from a large degeneracy of states and a frustration induced by doping the antiferro magnet.
We review recent results for the properties of doped antiferromagnets, obtained by the numerical analysis of the planar t-J model using the novel finite-temperature Lanczos method for small correlated systems. First we briefly summarize our present understanding of anomalous normal-state properties of cuprates, and present the electronic phase diagram, phenomenological scenarios and models proposed in this connection. The numerical method is then described in more detail. The following sections are devoted to various static and dynamical properties of the t-J model. Among the thermodynamic properties the chemical potential, entropy and the specific heat are evaluated. Discussing electrical properties the emphasis is on the planar optical conductivity and the d.c. resistivity. Magnetic properties involve the static and dynamical spin structure factor, as measured via the susceptibility measurements, the NMR relaxation and the neutron scattering, as well as the orbital current contribution. The analysis of electron spectral functions, studied by photoemission experiments, and their relation to the c-axis conductivity, follows. Finally we discuss density fluctuations, the electronic Raman scattering and the thermoelectric power. Whenever feasible a comparison with experimental data is performed. A general conclusion is that the t-J model captures well the main features of anomalous normal-state properties of cuprates, for a number of quantities the agreement is even a quantitative one. It is shown that several dynamical quantities exhibit at intermediate doping a novel universal behaviour consistent with a marginal Fermi-liquid concept, which seems to emerge from a large degeneracy of states and a frustration induced by doping the antiferro magnet.
Finite-temperature spin dynamics in the planar $t\ensuremath{-}J$ model are studied using a method based on the Lanczos diagonalization of small systems. The dynamical spin structure factor at moderate dopings shows the coexistence of free-fermion-like and spin-fluctuation time scales. At T<J, low-frequency and static susceptibilities show a pronounced T dependence, supporting a scenario related to the marginal Fermi liquid one, for the explanation of neutron-scattering and NMR relaxation experiments in cuprates. Calculated NMR relaxation rates reasonably reproduce experimental ones.
Recent results for the finite-temperature static and dynamical properties of the planar t−J model, obtained by a novel numerical method for small correlated systems, are reviewed. Of particular interest are T>0 charge and spin response functions: optical conductivity σ(ω) and spin susceptibility χ(q,ω), which show very universal features at intermediate doping. In spin dynamics the universality is best seen in the local spin correlation function, which appears to be T-independent and only weakly doping dependent. Results apply directly to the inelastic neutron scattering and to the NMR relaxation experiments in cuprates. Analysing σ(ω) we find that the current correlation function C(ω) is nearly T- and moreover ω-independent in the regime $T
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.
Charge and spin response in the planar $t\ensuremath{-}J$ model at finite temperatures are investigated numerically, in the regime corresponding to cuprates at intermediate doping. We show that the local spin correlation function is T independent, leading to ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega}<J)\ensuremath{\propto}\mathrm{tanh}(\ensuremath{\omega}/2T)$. The current correlation function $C(\ensuremath{\omega})$ appears to be T as well as $\ensuremath{\omega}$ independent, and the optical conductivity $\ensuremath{\sigma}\ensuremath{\propto}({1\ensuremath{-}e}^{\ensuremath{-}\ensuremath{\omega}/T})/\ensuremath{\omega}$. Such anomalous response functions are brought in connection with the large entropy persisting at T<J.
We systematically examine the asymmetry of the electronic states in the hole- and electron-doped cuprates by using a $t\text{\ensuremath{-}}J$ model with the second-neighbor hopping ${t}^{\ensuremath{'}}$ and third one ${t}^{\ensuremath{''}}$ (the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model). Numerically exact diagonalization method is employed for a 20-site square lattice. We impose twisted boundary conditions (BC) instead of standard periodic BC. For static and dynamical correlation functions, averaging procedure over the twisted BC is used to reduce the finite-size effect. We find that antiferromagnetic spin correlation remains strong in electron doping in contrast to the case of hole doping, being similar to the case of the periodic BC. This leads to a remarkable electron-hole asymmetry in the dynamical spin structure factor and two-magnon Raman scattering. By changing the twist, the single-particle spectral function is obtained for all momenta in the Brillouin zone. Examining the spectral function in detail, we find a gap opening at around the $\mathbf{k}=(\ensuremath{\pi},0)$ region for 10% doping of holes (the carrier concentration x=0.1), leading to a Fermi arc that is consistent with experiments. In electron doping, however, a gap opens at around $\mathbf{k}=(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and persists up to x=0.2, being correlated with the strength of the antiferromagnetic correlation. We find that the magnitude of the gaps is sensitive to ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$. A pseudogap is also seen in the optical conductivity for electron doping, and its magnitude is found to be the same as that in the spectral function. We compare calculated quantities with corresponding experimental data, and discuss similarities and differences between them as well as their implications.
Several thermodynamic quantities within the planar $t\ensuremath{-}J$ model are calculated using the T>0 Lanczos method on clusters of up to 26 sites. The hole density ${c}_{h}(\ensuremath{\mu},T)$ shows a non-Fermi-liquid behavior as a function of T and suggests a transition from small to large Fermi surfaces at ${c}_{h}\ensuremath{\sim}0.15$. The specific heat reveals a maximum at the exchange energy scale up to ch=0.2, where it becomes almost T independent for $T\ensuremath{\gtrsim}0.15t$. At constant T the entropy has maximum for ${c}_{h}\ensuremath{\sim}0.15$ with large values at low T, consistent with experiments on cuprates. In the underdoped regime the spin susceptibility ${\ensuremath{\chi}}_{0}(T)$ exhibits a maximum at finite T=T∗, with T∗ decreasing with doping and disappearing for ch>0.15.