We investigate the effects of the next-nearest-neighbor (t') and the third-nearest-neighbor (t") hopping terms on superconductivity correlation in the 2D hole-doped extended t-J model based on the variational Monte Carlo, mean-field calculation and exact diagonalization method. Despite the diversity of the methods employed, the results all point to a consistent conclusion: While the d-wave superconductivity correlation is slightly suppressed by t' and t" in underdoped regions, it is greatly enhanced in the optimal and overdoped regions. The optimal Tc is a result of the balance of these two opposite trends.

The dispersion of a single hole in the t-J model obtained by the exact result of 32 sites and the results obtained by self-consistent Born approximation and the Green function Monte Carlo method can be simply derived by a mean-field theory with d-wave resonating-valence-bond (d-RVB͒ and antiferromagnetic order parameters. In addition, it offers a simple explanation for the difference observed between those results. The presence of the extended van Hove region at (,0) is a consequence of the d-RVB pairing instead of the antiferromagnetic order. Results including tЈ and tЉ are also presented and explained consistently in a similar way. ͓S0163-1829͑97͒08701-8͔Important advances in the study of high-temperature superconductors have been made recently by angle-resolved photoemission ͑ARPES͒ experiments.1,2 Extended van Hove singularity ͑EVHS͒ near the Fermi surface of the superconductors is found. In particular, Wells et al. 3 have measured the ARPES for the insulating Sr 2 CuO 2 Cl 2 and find good agreement with the prediction of the t-J model about the bandwidth and other features. Although there is substantial disagreement about the position of the energy level near (,0͒.There were many theoretical studies 4 of the properties of a single hole in a quantum antiferromagnet. The theoretical data used in comparison with ARPES data are obtained from the t-J model by using the self-consistent Born approximation ͑SCBA͒ 5-7 to treat the scattering of a single hole with the spin waves of the Néel state. The result of SCBA shows an EVHS near (,0). The SCBA dispersion of the single hole is also reproduced in the Green function Monte Carlo ͑GFMC͒ approach by Dagotto et al. 8 Based on these results, Dagotto and collaborators 9 have argued that the EVHS is due to the antiferromagnetism and have proposed the antiferromagnetic van Hove theory to explain the mechanism of superconductivity.Recently Leung and Gooding 10 have solved the spectra exactly for a single hole in a 32-site square cluster. The dispersion relation obtained is very similar to the result of SCBA except they have not observed the exact symmetry resulted from folding the Brillouin zone ͑BZ͒ in half due to the antiferromagnetic long-range order. It should be noticed that this asymmetry is also observed in the GFMC result 8 for a 12ϫ12 cluster.In this paper we will show that the results obtained by SCBA ͑Ref. 7͒ and GFMC ͑Ref. 8͒ as well as exact diagonalization 10 can be easily reproduced by a mean-field theory including both d-wave resonating-valence-bond (d-RVB͒ and antiferromagnetic order parameters. The presence of the EVHS is associated with the d-RVB pairing.We have also looked at a more general t-J model by including next-nearest-neighbor hopping, tЈ, and next-nextnearest-neighbor hopping, tЉ. It is shown below that the complicated dispersions obtained by including tЈ and tЉ are easily understood in terms of the mean-field theory. A better agreement with the ARPES of the insulating Sr 2 CuO 2 Cl 2 ͑Ref. 3͒ could be obtained by tuning the values of tЈ and ...

We have developed an algorithm that combines the concept of optimization with the conventional hybrid input-output ͑HIO͒ algorithm for phase retrieval of oversampled diffraction intensities. In particular, the optimization algorithm of guiding searching direction to locate the global minimum has been implemented. Compared with HIO, this guided HIO algorithm retrieves the lost phase information from diffraction intensities with much better accuracy.

A path-integral approach to the Hubbard model is developed for the whole range of the coupling strength U. At half filling, the strong-coupling results are readily reproduced within the simple Gaussian fluctuations.The low-lying spin wave is shown to be described by the nonlinear a (2) it also agrees with the t-J-model result. The present method provides a starting point to approach the finitedoping problem.