First principles pseudopotential method based on density functional theory is used to investigate the Structural, Mechanical, Phonon, Thermodynamic and Electronic properties of Mg2Sn. The equilibrium properties including lattice constant, bulk modulus, pressure derivative cohesive energy, young modulus, shear modulus were determined. The results obtained were compared with available experimental and other available results. Mg2Sn was found to be brittle in nature with a non-metallic properties as shown by the value of the Cauchy pressure of -4.03. The Phonon dispersion curve of Mg2Sn was obtained utilizing the PBE-GGA exchange-correlation potential as employed in the Vienna Ab-Initio Simulation Package (VASP) computer code. The gap separating the acoustic and the optical branch of the curve was found to be about 50cm-1 at X-point. The thermodynamic properties of the material was investigated in the temperature of 0-800K. At room temperature, the calculated value of the specific heat capacity ( ) is 71.28J/mol which is in good agreement with experimental and other results. Mg2Sn was found to a narrow gap semiconductor with an indirect bandgap of magnitude of 0.175eV.

We calculated the structural, electronic, mechanical and thermal properties of Fe3Al semiconducting using Quantum ESPRESSO, an open source first principles code based on density-functional theory, plane waves, and pseudopotentials. Structural parameter results (equilibrium lattice parameters, bulk modulus and its derivative pressure) have been reported. The underestimated band gap is obtained along with higher state density and energy bands around the fermi level. Mechanical properties of the rock-salt structure of Fe3Al, such as, shear modulus (G), Young’s modulus (E), and Poisson’s ratio () were investigated. The thermodynamic parameters are also present. The results are in good agreement with the available experimental and other theoretical results.

The periodic Anderson model is applied to 4 electrons on 4 sites with periodic boundary conditions. We applied magnetic field to the localized forbitals, Eσf. The number of electrons is taken to be one per site and the interactions between different sites is restricted to nearest neighbors. The many body eigenvalues are calculated exactly using exact diagonalization technique. We find that the specific heat is suppressed by the variation of the band energy of the localized f-orbitals as mediated by the application of the magnetic field, H, under various hybridization energy. A continuous suppression of the specific heat reduces the heavy fermion behavior in the system.

In this work, we applied density matrix renormalization group to one-dimensional Hubbard model at five numbers of sweep to solve strongly correlated interacting electrons system, starting from two electrons on two sites up to ten electrons on ten sites at half filling. The results that emerged from the present study is in agreement with that of exact diagonalization, variational and Lanczos solution at the varying values of the Coulomb interaction strength (U/t) at t=1. The total energy, E g /t, of the ground state increases with the increase in interaction strength for all the numbers of site, N. The spectra intensity increases with increase in the interaction strength but decreases to zero when the interaction strength is made negatively large. This study is extended to more than two electrons on two sites. We equally show effect of interaction strength, U/t, at t = 1 on the energy-dependent entropy, S.