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Physical review. B, Condensed matter

Exact-diagonalization study of the spectral-weight functions and the density of states of the lattice Anderson model

J. Callaway, J. W. Kim, L. Tan, Hsueh‐Ju Lin

Published Oct 15, 1993• 14 citations
Publisher

Abstract

We report numerical calculations of the spectral-weight functions for the lattice Anderson model on small clusters of square and tetrahedral geometry by exact diagonalization. Parameters in the weak-hybridization--strong-interaction sector are considered. The behavior of the f levels is studied as the occupancy varies from the doubly occupied limit to the nearly empty case.

DOI
10.1103/physrevb.48.11545

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We report numerical calculations of the spectral-weight functions for the lattice Anderson model on small clusters of square and tetrahedral geometry by exact diagonalization. Parameters in the weak-hybridization--strong-interaction sector are considered. The behavior of the f levels is studied as the occupancy varies from the doubly occupied limit to the nearly empty case.
The lattice Anderson model is considered with two nondegenerate orbitals per site (c and f ). The Hamiltonian matrix is constructed in a localized representation on a four site, tetrahedral cluster. All the eigenvalues are obtained for any occupancy by explicit diagonalization, using symmetry to reduce the problem to manageable size. Thermodynamic functions are calculated. Emphasis in this work is placed on the strong interaction–weak hybridization sector of the model. The behavior of the model is quite complex, with five different regions delineated.
The spectral weight function A(p,\ensuremath{\omega}) and density of states D(\ensuremath{\omega}) at half filling are calculated with an exact diagonalization technique on the 4\ifmmode\times\else\texttimes\fi{}4 square lattice in the one-band Hubbard model from weak to strong coupling. Quasiparticle peaks are observed at weak and moderate couplings, while mostly incoherent structure appears at strong coupling. The gap in the density of states can be observed for all couplings and widens as the interaction strength increases.
We report the results of a calculation of the spectral weight function of a single hole (or electron) placed in an otherwise half-filled band described by the one-orbital Hubbard model. The calculation is made by exact diagonalization. An eight-site cubic cluster is considered. The density of states is studied as the interaction strength is varied between weak and strong couplings. We observe the spreading of the spectral weight associated with some single-particle eigenstates over a large range of energies, and the appearance of satellite structure at higher excitation energies. Only modest band narrowing is found.
Abstract We investigate the ground state properties and the energy level statistics of a two-dimensional 3 × 3 square lattice cluster of simple and extended Hubbard model in parameters space − 10 ≤ U, V ≤ 10 for various electron configurations (N e = 10, 8, 6 and 4) within the spin subspace S = 0 using exact diagonalization. In simple Hubbard model, we observe transition from a behavior where electrons remain correlated to lattice sites to electron-paired state as U is varied from positive to negative. In case of extended Hubbard model, we observe tendency for SDW ordering (enhanced by negative V) and CDW ordering (favored by positive V), modulated by electron density. The spectral properties of energy level statistics, analyzed using kernel density estimation, reveal a complex interplay between level attraction and level repulsion, highlighting the tunability of these properties through interaction parameters.
Two very different methods — exact diagonalization on finite chains and a variational method — are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied d sites (gn d ) as a function of various parameters. In the absence of on-site Coulomb interaction (U f ) between f electrons, the two methods yield similar results. The double occupancy of d levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite U f , while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value (U ), which depends on U f and V.