Second-order electronic correlation effects in a one-dimensional metal

The Pariser-Parr-Pople (PPP) model of a single-band one-dimensional (1D) metal is studied at the Hartree-Fock level, and by using the second-order perturbation theory of the electronic correlation. The PPP model provides an extension of the Hubbard model by properly accounting for the long-range character of the electron-electron repulsion. Both finite and infinite version of the 1D-metal model are considered within the PPP and Hubbard approximations. Calculated are the second-order electronic-correlation corrections to the total energy, and to the electronic-energy bands. Our results for the PPP model of 1D metal show qualitative similarity to the coupled-cluster results for the 3D electron-gas model. The picture of the 1D-metal model that emerges from the present study provides a support for the hypothesis that the normal metallic state of the 1D metal is different from the ground state.Comment: 21 pages, 16 figures; v2: small correction in title, added 3 references, extended and reformulated a few paragraphs (detailed information at the end of .tex file); added color to figure

Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems

Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries and characterizations of strongly correlated electron materials and by requirements for understanding mechanisms of intriguing phenomena beyond a single-particle picture. A three-stage scheme is developed as renormalized multi-scale solvers (RMS) utilizing the hierarchical electronic structure in the energy space. It provides us with an ab initio downfolding of the global band structure into low-energy effective models followed by low-energy solvers for the models. The RMS method is illustrated with examples of several materials. In particular, we overview cases such as dynamics of semiconductors, transition metals and its compounds including iron-based superconductors and perovskite oxides, as well as organic conductors of kappa-ET type.Comment: 44 pages including 38 figures, to appear in J. Phys. Soc. Jpn. as an invited review pape

Variational determination of the two-particle density matrix : the case of doubly-occupied space

The world at the level of the atom is described by the branch of science called quantum mechanics. The crown jewel of quantum mechanics is given by the Schrödinger equation which describes a system of indistinguishable particles, that interact with each other. However, an equation alone is not enough: the solution is what interests us. Unfortunately, the exponential scaling of the Hilbert space makes it unfeasible to calculate the exact wave function. This dissertation concerns itself with one of the many ab initio methods that were developed to solve this problem: the variational determination of the second-order density matrix. This method already has a long history. It is not considered to be on par with best ab initio methods. This work tries an alternative approach. We assume that the wave function has a Slater determinant expansion where all orbitals are doubly occupied or empty. This assumption drastically reduces the scaling of the N-representability conditions. The downside is that the energy explicitly depends on the used orbitals and thus an orbital optimizer is needed. The hope is that by using this approximation, we can capture the lion's share of the static correlation and that any missing dynamic correlation can be added through perturbation theory. We developed an algorithm based on Jacobi rotations. The scaling is much more favorable compared to the general case. The method is then tested on a array of benchmark systems

Ab-initio Electronic Structure Method for Substitutional Disorder Applied to Iron-Based Superconductors

An ab-initio electronic structure method for substitutionally disordered real materials is developed within a pseudopotential density functional theory approach. The method is validated against exact diagonalization and for simple disordered CuZn alloys. The developed method is applied to iron-based superconductors. In particular, band renormalization effects due to various chemical substitutions in BaFe₂As₂ are investigated and their Cooper pair breaking effects are compared

Variational and Diffusion Quantum Monte Carlo Calculations with the CASINO Code

We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the CASINO program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and software and discussing their strengths and their weaknesses. We review a range of recent applications of CASINO