Numerical Research About One-Dimensional Hubbard Superlattice

Strongly correlated electronic system is still the active focus of interest in con-densed matter physics until now. Only a few of strongly correlated electronic models can be exactly solved and numerical techniques are used to understand the effect of electron interaction in many systems. Density matrix renormalization group is an ac-curate and effective numerical method for low-dimensional strongly correlated systems. For considerable insight into the effect of nanoscale spatial inhomogeneity in strong-ly correlated systems, we study the physical properties of one-dimensional half-filled Hubbard superlattices. The Hubbard super lattices here have LU repulsive (repulsive interaction U>0 and orbital energy ?? 0) and L0 free (U=?= 0) sites per unit cell. In this thesis, we have fixed LU= 1 and different L0. It's found that the properties of Hubbard superlattices have an odd-even L0. disparity.The superlattices with odd Lo have the incommensurate charge density wave near the particle-hole symmetric point and the charge density wave is always commensurate for even L0. The incommensurate charge density wave results from the collective ad-vantage of the charge correlations with even distance over ones with odd distance. For odd L0, the superlattice is metal at the particle-hole symmetric point and it turns into band insulator beyond this point. For even L0 and under the particle-hole symmetry, the system has an metal-insulator transition from metal to Mott insulator with U in-creasing and it's still metal far away from the particle-hole symmetric point. Multiple peaks appear in the spin density wave structure factor for even Lo because of the strong antiferromagnetic correlation between nearest neighbouring repulsive sites.To confirm the conclusion from density matrix renormalization group, the super-lattice Hamiltonian is also investigated by Hartree-Fock approximation, the equation of motion of double-time Green function technique and cluster perturbation theory. The superlattice with L0=1 is described well in energy band theory and the above three methods are qualitatively correct. The superlattice with L0=2 has obvious strong correlation effect and only the conclusion of the Green function technique and cluster perturbation theory coincides qualitatively with that from density matrix renormal-ization group. The single-particle spectral weight calculated from cluster perturbation theory has more details compared with the spectral function given by the Green func-tion technique. When U is weak, the spectral weight has the similar aspect with the energy band of non-interacting system. With a large U and because of the strong an-tiferromagnetic correlation, the band has the gaps opening at k=±?/2 and displays the same character with the single-particle spectral weight of one-dimensional Hubbard model.