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In a simple model we investigate three competing orders: d-wave superconductivity, spin and orbital antiferromagnetism (AF) in the vicinity of a single vortex in a cuprate superconductor. We find that when the potential for the orbital AF $V_{d}$ is comparatively small, the spin-density-wave (SDW) order has an enhancement at the vortex core center, and the ''d-density-wave'' (DDW) order exhibits a rather weak behavior around the core and vanishing small away from the core. However, when $V_{d}$ becomes large, globally, the SDW order decreases and the DDW order increases; locally, not only the peak of the SDW order around the core still exists, though relatively suppressed, but also a local peak for the DDW order finally appears. Similar effects are also revealed for the features when varying doping. Comparisons with experiments are discussed., Comment: 4 PS figures

For a class of quasi-one-dimensional clusters, by using exact diagonalization, we study the effect of side spins on the spin-spin correlations on chain. Our calculations show that the side spins added in the same sublattice can effectively strengthen the spin-spin correlations in large distance region and make the change tend to flat. It is exactly proved that periodically adding side spins can set up magnetic long-range orders in the ground state. Also we investigate the effect of the density of side spins on correlation strength. The case that two sublattices have different localized spins is discussed., Comment: accepted by Journal of Physics: Condensed Matter

By exact diagonalization, we investigate several spin-$\frac 12$ $J_1-J_2$ real clusters of molecular scale with different shapes. Our calculations show that when the ratio, $\eta $, of next nearest neighbor to nearest neighbor bonds is equal to 1, even the cluster of only 25 sites exhibits the bulk behaviors and has the quantum phase transitions. Two effective critical points are around $J_2/J_1=0.3762$ and 0.612 respectively. They are very close to those of the infinite $J_1-J_2$ square lattice. But, when $\eta \leq 0.85$, the quantum phase transition around $J_2/J_1=0.3762$ disappears. By calculating the distributions of the average values of $S_i^z$, the bulk behaviors are demonstrated graphically. In the intermediate phase, the sites on the corners have distinctly different character from the other sites. The distribution is obviously centralized on the corner sites., Comment: 4 pages, 3 figures, Accepted for publication in Phys. Rev. B

The doping and frequency evolutions of the incommensurate spin response and the resonance mode are studied based on the scenario of the Fermi surface topology. We use the slave-boson mean-field approach to the $t-t^{\prime}-J$ model and including the antiferromagnetic fluctuation correction in the random-phase approximation. We find that the equality between the incommensurability and the hole concentration is reproduced at low frequencies in the underdoped regime. This equality observed in experiments was explained {\it only} based on the stripe model before. We also obtain the downward dispersion for the spin response and predict its doping dependence for further experimental testing, as well as a proportionality between the low-energy incommensurability and the resonance energy. Our results suggest a common origin for the incommensuration and the resonance peak based on the Fermi surface topology and the d-wave symmetry., Comment: 5 pages, 4 PS figures

We study single hole motion in LaMnO$_3$ using the classical approximation for JT lattice distortions, a modified Lang-Firsov approximation for dynamical breathing-mode phonons, and the self-consistent Born approximation (verified by exact diagonalization) for hole-orbital-excitation scattering. We show that in the realistic parameter space for LaMnO$_3$, quantum effects of electron-phonon interaction are small. The quasiparticle bandwidth $W \simeq 2.2J$ in the purely orbital t-J model. It is strikingly broadened to be of order $t$ by strong static Jahn-Teller lattice distortions even when the polaronic band narrowing is taken into account., Comment: 4 pages, 4 eps figures

Based on the slave-boson theory of the two-dimensional $t-t'-J$ model, we calculate the superconducting condensation energy for optimally doped and overdoped high $T_{c}$ cuprates at finite temperatures using a renormalized random phase approximation. The contributions come from the mean-field part and the antiferromagnetic spin fluctuations. In the presence of neutron resonance peak at $(\pi,\pi)$, the latter is shown to have similar temperature and doping dependences as the difference in antiferromagnetic (AF) exchange energy between the normal and the superconducting state. This difference has been proposed to be related to the superconducting condensation energy by Scalapino and White. The total condensation energy, however, is about 1/2 smaller than the proposed AF exchange energy difference and shows a more rapid decrease as the temperature rises. The doping dependence of the condensation energy is found to be consistent with experiments. In particular, near zero temperature, our result shows a good quantitative agreement with experiments., Comment: 6 pages, 7 figures in ps files

By use of the orbital t-J model, we calculate the photoemission spectra of LaMnO3 using the exact diagonalization technique, and interpret our numerics quite well in the orbital-polaron scenario where the scattering between holes and orbital excitations is treated within the self-consistent Born approximation. The quasiparticle bandwidth is found to be of the order of J and t in the purely Coulombic and Jahn-Teller phononic model, respectively. We suggest that angle-resolved photoemission spectroscopy experiments allow one to distinguish between the orbital-polaron scenario and the Jahn-Teller polaron scenario., Comment: 5 pages with 4 eps figures. RevTeX 3.1. Correct two typos

The effects of nonmagnetic impurity on the spin excitation spectra in a $d_{x^2-y^2}$-wave superconductor are examined, using the self-consistent $t$-matrix approximation. It is shown that the impurity self-energy acts to shift the position of the resonance peak to low frequencies and broaden the peak. While the impurity vertex correction causes a broad spectral weight in the spin gap at the impurity concentrations where no clear resonance peak is observed. The gaplike feature still remains in low frequency region upon the introduction of impurities. Incorporating these two effects, we find that the result is in qualitative agreement with experiments on YBa_{2}(Cu_{1-x}Zn_{x})_{3}O_{6+y}., Comment: 6 pages, 4 figures (Fig.3 is available upon request)