The precursor of the metal-insulator transition is studied at ab initio level in linear chains of equally spaced lithium atoms. In particular, full configuration interaction calculations (up to 1 x 10(9) determinants) are performed, in order to take into account the different nature of the wave function at different internuclear distances. Several indicators of the Metal-Insulator transition (minimum of the energy gap, maximum of the localization tensor or of the polarizability) are considered and discussed. It is shown that the different indicators give concordant results, showing a rapid change in the nature of the wave function at an internuclear distance of about 7 bohrs.
The precursor of the metal-insulator transition is studied at ab initio level in linear chains of equally spaced lithium atoms. In particular, full configuration interaction calculations (up to 1 x 10(9) determinants) are performed, in order to take into account the different nature of the wave function at different internuclear distances. Several indicators of the Metal-Insulator transition (minimum of the energy gap, maximum of the localization tensor or of the polarizability) are considered and discussed. It is shown that the different indicators give concordant results, showing a rapid change in the nature of the wave function at an internuclear distance of about 7 bohrs.
The precursor of the Metal-Insulator transition is studied at ab-initio level in equally-spaced Li n and Be n linear chains. In particular, large-size Full Configuration-Interaction (FCI) calculations (up to one billion determinants for Li 8 and half a billion for Be 5 ) have been performed. At FCI level, it is possible to take into account the different nature of the electronic wavefunction at the different internuclear distances. Several indicators of the Metal-Insulator transition (minimum of the Koopmans energy gap, maximum of the localization and polarizability tensors) are considered and discussed. In is shown that the three considered properties indicate a Metal-Insulator transition at distances that are in remarkable agreement.
We have studied the metal--insulator-like transition in pseudo-one-dimensional systems, i.e., lithium and beryllium rings, through the ab initio density matrix renormalization group (DMRG) method. Performing accurate calculations for different interatomic distances and using quantum information theory, we investigated the changes occurring in the wave function between a metallic-like state and an insulating state built from free atoms. We also discuss entanglement and relevant excitations among the molecular orbitals in the Li and Be rings and show that the transition bond length can be detected using orbital entropy functions. Also, the effect of different orbital bases on the effectiveness of the DMRG procedure is analyzed comparing the convergence behavior.
The clear distinction between metals and insulators is a well established and appartently simple concept which can be clarified by studying the behavior of the electrical conductivity. However, a theoretical description of the processes leading to one of the two extremes is no trivial task. The widely accepted band structure theory relies on an one-electron picture to characterize the metallic/insulating behavior of a material. However, in spite of the fact that it can be used to make successful predictions, this description does not capture one of the essential elements characterizing the nature of an electronic quantum system, i.e. the electron correlation. The key to the different behaviors is clearly contained in the correlated many- electron wave function, but the analysis of such a high-dimensional object in configuration space can be quite cumbersome. Therefore the development of powerful tools to simplify this task is necessary. The total position-spread (TPS) tensor, which was derived by Walter Kohn’s theory of the insulating state, plays a key role in the field of metal-insulator transitions (MITs). This tool provides information about the electron localization, which is strongly connected to the electrical conductivity. Therefore, in this work particular attention was paid to the calculation of the TPS tensor of small and extended systems. Moreover, part of this thesis focuses on a new formalism, which allows the study of spin mobility and spin entanglement and provides therefore deeper insight into the effects of electron correlation. In the framework of quantum information theory (QIT), the quantum entanglement can be quantified by means of measures such as the von Neumann entropy. Also, the analysis of the elements of the two-orbital reduced density matrix provides an overview of the complexity of the many-electron wave function. These insights were used in this work for the analysis of the metallic/insulating character of a system. However, in order to perform such investigastions, the problem of achieving an accurate description of the many- electron wave function has to be dealt with. Despite the tremedous progress in the efficiency of quantum-chemical methods, the treatement of extended systems using standard approaches is still a difficult (if not unfeasible) task. Therefore the development and testing of sophisticated, low-scaling methods is currently the subject of many investigations. In this work, two approaches were employed: 1) the ab-initio density matrix renormalization group (DMRG) approach which, based on a tensor product ansatz, provides very precise results and exploits QIT to improve its performance; 2) the method of increments (MoI) which, using a many-body expansion in terms of localized orbitals, yields accurate correlation energies. By using both methods on strongly correlated one-dimesional model systems, we worked on a new formalism of the method of increments which can be used to describe the whole dissociation curve without inconvenient discontinuities. Finally, aiming to calculate the total position-spread tensor of extended systems, we worked on the application of the MoI for quantities other than the correlation energy.
The linear chain of hydrogen atoms, a basic prototype for the transition from a metal to Mott insulator, is studied with a recent density functional theory model functional for nondynamic and strong correlation. The computed cohesive energy curve for the transition agrees well with accurate literature results. The variation of the electronic structure in this transition is characterized with a density functional descriptor that yields the atomic population of effectively localized electrons. These new methods are also applied to the study of the Peierls dimerization of the stretched even-spaced Mott insulator to a chain of H 2 molecules, a different insulator. The transitions among the two insulating states and the metallic state of the hydrogen chain system are depicted in a semiquantitative phase diagram. Overall, we demonstrate the capability of studying strongly correlated materials with a mean-field model at the fundamental level, in contrast to the general pessimistic view on such a feasibility.
The Simplest Density-Driven Transition The simplest metal–insulator (MI) transition is that due to band filling (or emptying) in a system of non-interacting electrons. This is the fermionic equivalent of Bose–Einstein condensation in a system of non-interacting bosons. Let us consider a system of non-interacting electrons described by a tight-binding band in a hyper-cubic lattice in d -dimensional space. As the number of electrons per site n , for a given spin direction, approaches the value n c = 1 the system evolves from a metallic to an insulating state. This transition is a quantum critical phenomenon with which we can associate critical exponents. We can introduce a characteristic length χ , which can be identified with a screening length which diverges at the metal–insulator transition. The natural variable to describe this zero-temperature transition is the distance from the chemical potential or Fermi level μ , to the bottom, E b = 0, or to the top of the band E t , i.e. g = μ − E b,t . In terms of this variable, ξ ∝ | g | − ν and the ground state free energy density has a singular part that behaves as, f ∝ | g | 2− α , close to the transition. This expression defines the critical exponent α . The critical exponents ν and α associated with this zero temperature transition are related through the quantum hyperscaling relation 2 − α = ν ( d + z ). For this simple MI transition it is possible to determine its universality class for any dimension (Continentino, 1995a). One starts by noticing that the gap for excitations is actually a linear function of the distance g = μ − E t . This fixes the gap exponent at the value νz = 1. Furthermore, for a hypercubic lattice the density of states close to the band edges varies as, such that, the number where μ is the chemical potential.