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The presence of long-range spin and charge correlations underlies a variety of physical phenomena in condensed-matter systems, especially, in qubits systems. This work aims to study quantum entanglement versus spin and charge correlations in qubits systems modeled by 1D Extended Hubbard Model. The considered model is parameterized by on-site coulomb interaction energy U, off-site coulomb interaction energy V and exchange spin-spin interaction γJ, where γ is the anisotropy parameter. In charge space, the quantum entanglement reaches its maximum value for an optimal interatomic distance that checks the condition U = 2V. Moreover, in spin phase the quantum entanglement increases with external magnetic field h, especially, for anisotropic Ising model with γ = 1.

Metal-insulator and CDW-SDW transitions are studied in the one-dimensional Extended Hubbard Model at half-filling by analysing the behaviour of local entanglement in fermionic systems. 1D traditional Hubbard model exhibits metal-insulator transition at critical point Uc = 0, where local entanglement reaches its maximum value. Moreover, a transition between charge- and spin-density- wave (CDW-SDW) occurs in 1D Extended Hubbard Model tUV with long-range interaction at straight line U = 2 V. The analysis of our obtained results shows that CDW-SDW transition has curious properties whose can be used in quantum information processing.

In this work, we proved the Cosine Rule II for a spherical triangle on the dual unit sphere

In plane Lorentzian geometry it is studied points, timelike, spacelike and lightlike lines, triangles, etc [4]. On the hyperbolic sphere, there are points, but there are no straight lines, at least not in the usual sense. However, straight timelike lines in the Lorentzian plane are characterized by the fact that they are the shortest paths between points. The curves on the hyperbolic sphere with the same property are hyperbolic circles. Thus it is natural to use these circles as replacements for timelike lines. The formulas for the sine and cosine rules are given for the Euclidean sphere 2 S [2, 3, 6] and hyperbolic sphere [5]. In this study, we obtained formulas related with the spacelike angles and hyperbolic angles corresponding to the sides of geodesic triangles on hyperbolic unit sphere \(H_{0}^{2}\).

In this work, we proved the sine and cosine rules for a spherical pure triangle on the dual Lorentzian unit sphere S ˜ 1 2 in the dual Lorentzian space D13.

In this paper. we obtain elementary abelian coverings of the regular hypermaps of genus 2 corresponding to the orientation-preserving automorphisın groups .$L2(3 ), the speciai linear group of order 24. and OK . the quaternion group of order 8. We also determine the reflexibility of these coverings.

In this work, we state and prove the sine, cosine I, cosine II, sine-cosine and cotangent rules for spherical triangles on the hyperbolic unit sphere H02 in the Lorentzian space R13.

In this paper, we obtain presentations for the non-equivalent regular unbranched Cp-coverings of a Klein Bottle by using the Reidemeister-Schreier method, where Cp =&lt, a | ap =1 &gt, is a cyclic group of order p (p is a prime).