Gutzwiller approximation applied to inhomogeneous lattice models and solid-state systems

The plan of this thesis is as follows. Chapt. 1 is devoted to the explanation of the main theoretical tool of our work, namely the GVM and GA. After introducing their earliest formulation by Martin C. Gutzwiller, we discuss their effectiveness in describing the physics of strongly correlated conductors, emphasizing the improvements they bring in comparison with mean-field, independent-electron approximations such as HF, and their limitations with respect to more refined, though computationally more costly, methods like DMFT and VQMC. We mention how the GA was initially exploited as an approximate tool for analytical calculation of expectation values on the GVW, and how later studies proved its exactness in the limit of infinite lattice coordination. After that, we discuss its more recent multi-band formulation which, together with the mixed-basis parametrization of Gutzwiller parameter matrix, is particularly important for combining the GVM with DFT. In Chapt. 2 we present our results for the strongly correlated Hubbard lattice with broken translational invariance due to the presence of a surface (panel (a) in Fig. 1), a metal-metal or metal-insulator junction (panel (b)), or a \u201csandwich\u201d of Mott insulator or strongly correlated metal between metallic leads (panel (c)). For all geometries, we show the layer dependence of the quasi-particle weight and provide approximate analytical fits for the data, together with a comparison with DMFT calculations on similar systems. In Chapt. 3, we introduce the formalism of DFT, the Kohn-Sham self-consistent equations for the functional minimization and the LDA for exchange and correlation functionals. We further discuss the performance and limitations of LDA and present the LDA+U method as a way to correct the self-interaction error of LDA. We explain the details of the GDF in Chapt. 4, and underline its similarities and differences with respect to the LDA+U functional. In the same chapter we present our data for paramagnetic and ferromagnetic bcc iron obtained through our implementation of LDA+G in the Siesta code. We show energy differences between spin-polarized and unpolarized Iron computed within LDA, GGA and LDA+G and with different basis sets. We compare the band structure, lattice parameters and magnetic moments (some sample data is shown in Table 1) obtained with these functionals, and discuss the implications of our results on the understanding of the origin of magnetism in transition metals. In the appendices we list some important results that we believed too detailed or too marginal to be presented in the main body of the thesis. Appendix A is devoted to some proofs and detailed explanations related to the GVM. In Appendix B we include all details related to the calculations on the layered geometries of Chapt. 2. In Appendix C we explain how to implement spin and orbital symmetries in the parametrization of the Gutzwiller projector, while in Appendix D we give the details of the minimization algorithm we implemented for optimizing the variational energy of the LDA+G calculation with respect to Gutzwiller parameters. Finally, Appendix E contains various topics of DFT and LDA+U that are important for the understanding of the GDF we implemented and discussed in Chapt. 4

Strongly correlated metal interfaces in the Gutzwiller approximation

We study the effect of spatial inhomogeneity on the physics of a strongly correlated electron system exhibiting a metallic phase and a Mott insulating phase, represented by the simple Hubbard model. In three dimensions, we consider various geometries, including vacuum-metal-vacuum, a junction between a weakly and a strongly correlated metal, and finally the double junctions metal-Mott insulator-metal and metal-strongly correlated metal- metal. We applied to these problems the self-consistent Gutzwiller technique recently developed in our group, whose approximate nature is compensated by an extreme flexibility,ability to treat very large systems, and physical transparency. The main general result is a clear characterization of the position dependent metallic quasiparticle spectral weight. Its behavior at interfaces reveals the ubiquitous presence of exponential decays and crossovers, with decay lengths of clear physical significance. The decay length of metallic strength in a weakly-strongly correlated metal interface is due to poor screening in the strongly correlated side. The decay length of metallic strength from a metal into a Mott insulator (or into vacuum) is due to tunneling. In both cases, the decay length is a bulk property, and diverges with a critical exponent ($\sim 1/2$ in the present approximation, mean field in character) as the (continuous, paramagnetic) Mott transition is approached.Comment: 19 pages, 19 figure

Chained activation of the motor system during language understanding

Two experiments were carried out to investigate whether and how one important characteristic of the motor system, that is its goal-directed organization in motor chains, is reflected in language processing. This possibility stems from the embodied theory of language, according to which the linguistic system re-uses the structures of the motor system. The participants were presented with nouns of common tools preceded by a pair of verbs expressing grasping or observational motor chains (i.e., grasp-to-move, grasp-to-use, look-at-to-grasp, and look-at-to-stare). They decided whether the tool mentioned in the sentence was the same as that displayed in a picture presented shortly after. A primacy of the grasp-to-use motor chain over the other motor chains in priming the participants' performance was observed in both the experiments. More interestingly, we found that the motor information evoked by the noun was modulated by the specific motor-chain expressed by the preceding verbs. Specifically, with the grasping chain aimed at using the tool, the functional motor information prevailed over the volumetric information, and vice versa with the grasping chain aimed at moving the tool (Experiment 2). Instead, the functional and volumetric information were balanced for those motor chains that comprise at least an observational act (Experiment 1). Overall our results are in keeping with the embodied theory of language and suggest that understanding sentences expressing an action directed toward a tool drives a chained activation of the motor system

Koopmans-compliant functionals and their performance against reference molecular data

Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate density-functional theory, these corrections give rise to orbital-density-dependent functionals and potentials. We show that the simplest implementations of Koopmans' compliance provide accurate estimates for the quasiparticle excitations and leave the total energy functional almost or exactly intact, i.e., they describe correctly electron removals or additions, but do not necessarily alter the electronic charge density distribution within the system. Additional functionals can then be constructed that modify the potential energy surface, including e.g. Perdew-Zunger corrections. These functionals become exactly one-electron self-interaction free and, as all Koopmans-compliant functionals, are approximately many-electron self-interaction free. We discuss in detail these different formulations, and provide extensive benchmarks for the 55 molecules in the reference G2-1 set, using Koopmans-compliant functionals constructed from local-density or generalized-gradient approximations. In all cases we find excellent performance in the electronic properties, comparable or improved with respect to that of many-body perturbation theories, such as G$_0$W$_0$ and self-consistent GW, at a fraction of the cost and in a variational framework that also delivers energy derivatives. Structural properties and atomization energies preserve or slightly improve the accuracy of the underlying density-functional approximations (Note: Supplemental Material is included in the source)

Essays on credit risk

The work investigates two major topics: the presence of a systematic and an idiosyncratic component in CDS spreads and the credit spread puzzle. We verify that a systematic factor is priced in the cross-section of CDS returns. We also notice that the systematic component of risk increases after the financial crisis. We finally verify that the fraction of systematic risk is not the same in different industrial sectors. In particular, more cyclical and systemic sectors show a much larger impact of the systematic factor. Regarding the second topic, we extend the literature proposing a bivariate state space model and verify that it actually improves the performances of standard inversion techniques in explaining the observed credit spreads. The improvement is particularly significant during the crisis period, characterized by a larger noise contaminating the observed equity price and equity volatility. This supports the ability of the state space model to remove the noise component and to produce better estimates of the asset value of the company and, consequently, more accurate predictions of spreads. In the last chapter we identify some explicit drivers for the noise postulated in the second paper. In particular, we verify that the errors produced by structural credit risk models significantly depend on liquidity indicators and that their explained variability is not negligible. We finally verify that the errors left by both structural variables and liquidity indicators are strongly correlated with market-wide measures of limits of arbitrage and/or deleveraging pressures

Pseudospin Magnetism in Graphene

We predict that neutral graphene bilayers are pseudospin magnets in which the charge density-contribution from each valley and spin spontaneously shifts to one of the two layers. The band structure of this system is characterized by a momentum-space vortex which is responsible for unusual competition between band and kinetic energies leading to symmetry breaking in the vortex core. We discuss the possibility of realizing a pseudospin version of ferromagnetic metal spintronics in graphene bilayers based on hysteresis associated with this broken symmetry.Comment: 5 pages, 4 figures; added figure 1, modified introduction and discussion; updated reference

Vision-Based Eye Image Classification for Ophthalmic Measurement Systems

: The accuracy and the overall performances of ophthalmic instrumentation, where specific analysis of eye images is involved, can be negatively influenced by invalid or incorrect frames acquired during everyday measurements of unaware or non-collaborative human patients and non-technical operators. Therefore, in this paper, we investigate and compare the adoption of several vision-based classification algorithms belonging to different fields, i.e., Machine Learning, Deep Learning, and Expert Systems, in order to improve the performance of an ophthalmic instrument designed for the Pupillary Light Reflex measurement. To test the implemented solutions, we collected and publicly released PopEYE as one of the first datasets consisting of 15 k eye images belonging to 22 different subjects acquired through the aforementioned specialized ophthalmic device. Finally, we discuss the experimental results in terms of classification accuracy of the eye status, as well as computational load analysis, since the proposed solution is designed to be implemented in embedded boards, which have limited hardware resources in computational power and memory size