Hubbard model is an important model in the theory of strongly correlated electron systems. In this contribution we introduce this model and the concepts of electron correlation by building on a tight binding model. After enumerating various methods of tackling the Hubbard model, we introduce the numerical method of exact diagonalization in detail. The book keeping and practical implementation aspects are illustrated with analytically solvable example of two-site Hubbard model.

Investigation of broken symmetry phases with long range order in strongly correlated electron systems is among subjects that have always been of interest to condensed matter scientists. In this paper we tried to study the existence of the 120 degrees magnetic spiral order, based on anisotropy in geometrically frustrated triangular lattices, using variational cluster approximation. We observed that by increasing the anisotropy in the system, the spiral order can be found for AWT IMAGE and for AWT IMAGE; however, it is limited by decreasing AWT IMAGE since antiferromagnetism is dominant for AWT IMAGE. Studying the Mott transition shows that a paramagnetic insulating phase, called quantum spin liquid, happens in the neighborhood of the spiral ordered phase.

Generalized Hubbard model was used to study the effect of uniaxial deformation of the vacancy defect in diamond. The [001] strain on the vacancy’s neighboring carbon atoms was assumed and in consequence the symmetry of crystal lowered to D2d. The results of Hubbard calculation with C70H70 cluster in the Gaussian 2003 package show that the T states (triplet spatial degenerate state) spilt to E (double spatial degenerate state) and A state (single spatial degenerate state). Also we found that the GR1 line in V0 will be changed by deformation percent of the vacancy’s neighboring carbon atoms and a little change in the ND1 line in the NV- which is in agreement with experimental results. Our results can predict the experimental results in this field.

We hereby introduce a research about a grand canonical ensemble for the extended two-site Hubbard model, that is, we consider the intersite interaction term in addition to those of the simple Hubbard model. To calculate the thermodynamical parameters, we utilize the nonextensive statistical mechan- ics; specifically, we perform the simulations of magnetic internal energy, specific heat, susceptibility, and thermal mean value of the particle number operator. We found out that the addition of the inter- site interaction term provokes a shifting in all the simulated curves. Furthermore, for some values of the on-site Coulombian potential, we realize that, near absolute zero, the consideration of a chemical potential varying with temperature causes a nonzero entropy.

In this work, we investigate the interacting electrons on a square lattice in the presence of Rashba spin-orbit coupling. We first obtain the effective spin model from the Rashba-Hubbard model in the strongly correlated limit using the second perturbation theory. The effective spin model includes isotropic Heisenberg terms, nearest-and next-nearest-neighbor interactions, as well as the anisotropic ones as Kane-Mele and Dzyaloshinski-Moriya interactions. We proceed to study the influence of Rashba spin-orbit coupling on the stability of the magnetic phases of isotropic Heisenberg using Luttinger-Tisza and variational minimization classical methods. Our classical calculations show that the anisotropic terms leads to the instability of the Neel, classical degenerate and collinear phases of the isotropic Heisenberg model on the square lattice into an incommensurate planar phase. The spiral magnetic order in the two-dimensional frustrated magnets can be disordered by considering the quantum fluctuations. In a heterostructure including a noncollinear magnet and a singlet superconductor, singlet Cooper pairs can be converted to triplet pairings due to the broken spin rotational symmetry. Therefore, we can engineer a topological superconductor using noncollinear magnet in a heterostructure system.

We study measurement induced disturbance (MID) in a qutrit-qutrit system with considering the e ect of the external magnetic  eld, nonlinear and lin-ear coupling constants and temperature. We show that all of these parameters have e ective roles in MID. We also investigate the e ect of  nite external magnetic  elds direction as parallel and anti-parallel on MID, and  nd some interesting results.

In this study, spin conductivity of gapped graphene using Hubbard model is calculated. We obtain spin conductivity for two cases: in the absence of coulomb interaction and in the presence of coulomb interaction between electrons. It can be seen that for the non-itercting case, by increasing the magnetization, the peaks of spin conductivity will be shifted towards lower frequencies and the height of them rises. By increasing the energy gap, the peaks of spin conductivity will be shifted towards higher frequencies and the height of them rises. In the interacting case, plots of spin conductivity versus frequency have two peaks. One of them belongs to spin up electrons and the other belongs to spin down electrons. By increasing magnetization, the peaks of spin up electrons will be shifted towards lower frequencies and the peaks of spin down electrons will be shifted towards higher frequencies. By increasing the repulsion coulomb interaction and the energy gap, spin up and spin down peaks will be shifted towards higher frequencies.

In this research the Hubbard parameters have been calculated for NiO and Gd crystals, as two strongly correlated systems with partially full 3d and 4f levels, respectively. The calculations were performed within the density functional theory (DFT) using the augmented plane waves plus the local orbitat (APW+lo) method. We constructed a suitable supercell and found that the Hubbard parameters for the NiO and Gd compounds are equal to 5.9 eV and 5.7 eV, respectively. Our results are in good agreement with experimental data and results of other computational methods.Then we used the obtained parameters to study the structural properties of NiO and Gd by means of LDA+U approximation. Our results calculated by the LDA+U method which are in better agreement with the experiment show a significant improvement compared to the GGA approximation. The result shows that our method for calculating U parameter can be considered as a satisfactory method to study a strongly correlated system.

We study the Mott transition in the two dimensional Hubbard model by using the variational cluster approximation. The transition potential obtained is roughly Uc» 2 and 6 for square and triangular lattices, respectively. A comparison between results of this approximation and other quantum cluster methods is presented. Our zero-temperature calculation at strong coupling show that the transition on the triangular and square lattices occur at lower values of U compared with other numerical techniques such as DMFT, CDMFT, and DCA. We also study the thermodynamic limit by an extrapolation to infinite size.

Plant development can be defined as a programmed qualitative change in plant form, which leads plant to maturity, and researchers call it as phasic development or phenology. Recognizing the timing of occurring each development stage is necessary for managing system in order to yield increment. The timing of occurring development stages depend on climate, genotype specifications and sowing date then determination of these times in different regions is difficult and it is only possible through the using of crop simulation models which can predict the timing of occurrence each development stage by integrating effective factors. The model was constructed based on linear equation of plant temperature response. In order to model evaluation two experiments were carried out in agricultural and natural resources research center of Khuzistan in 2003-2004 and 2004-2005 cropping years. Wheat development stages were determined based on Kirby and Appleyard’s scale by stereoscopic microscope and required GDD for each development stage as well. The constructed model was calibrated and run for simulation. Comparison of simulated and observed data showed that the model can strongly predict wheat development stages.