Ground State Energy of the Two Electrons on 2 Site of Aid Lattice Using the Lanczos Technique
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Abstract
Standard approaches to evaluate the ground-state properties of the Hubbard model via the Lanczos method have convergence problems upon the growing difference between hopping and Coulomb interaction strength. This issue is quite relevant since energy convergence does not necessarily translate into convergence of the ground state itself. The ground state energy and wave function of the single-band Hubbard model on the one-dimensional lattice is computed using the Lanczos methods. Ground state energy for two electron system on two sites was analytically solved using 4x4 matrixes. It is shown that the ground state energies obtained for different values of the interaction strength, compare nicely with that obtained using the method exact calculation.
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