Finite Size Effects in Correlated Electron Models

Thomas Hansen, Simon Vendelbo Bylling Jensen, Lars Bojer Madsen

Using the Hubbard model we study how the process of high-order harmonic generation (HHG) is modified by electron-electron correlation for both finite and bulk systems. A finite-size enhancement of the HHG signal is found and attributed to electrons backscattering off the lattice edges. Additionally, with the increasing strength of the electron-electron correlation an enhancement of the high-frequency regime of the HHG spectrum is found. This is attributed to the on-site Coulomb repulsion between electrons giving rise to a localized correlation-induced quiver motion of the electrons. The finite-lattice enhancement dominates the HHG spectra from a few harmonic orders until a threshold from which the correlational enhancement dominates. This threshold is determined by the degree of correlation and decreases into the low-frequency regime for increasing electron-electron correlation. This infers that as the electron-electron correlation increases, the finite-size effect on the electron dynamics decreases.

Hendra Kwee, Shiwei Zhang, Henry Krakauer

Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. A method is presented to correct for such errors. We show that MB FS effects can be effectively included in a modified local density approximation calculation. A parametrization for the FS exchange-correlation functional is obtained. The method is simple and gives post-processing corrections that can be applied to any MB results. Applications to a model insulator (P2 in a supercell), to semiconducting Si, and to metallic Na show that the method delivers greatly improved FS corrections.

Yukinori Ota, 太田 幸則

H. Schweitzer, G. Czycholl

Andrei A. Zvyagin

Quantum Spin- Chain with the Nearest-Neighbour Couplings Co-Ordinate Bethe Ansatz for a Heisenberg-Ising Ring Correlated Electron Chains: Co-Ordinate Bethe Ansatz Algebraic Bethe Ansatz Correlated Quantum Chains with Open Boundary Conditions Correlated Quantum Chains with Isolated Impurities Correlated Quantum Chains with a Finite Concentration of Impurities Finite Size Corrections in Quantum Correlated Chains Beyond the Integrability: Approximate Methods.