In this dissertation, we have presented our research on new developments in the Gutzwiller variational method as well as the applications of the method to two specific correlated electron systems of current interest: (i) the spinless fermion model with non-local Coulomb interaction in one dimension and (ii) the pressure-induced insulator-metal transition in the colossal magneto-resistive compound LaMnO3. Our results for the ground-state energy of the spinless fermion model are obtained by careful enumeration of the many-body configurations of the system and calculating the Gutzwiller reduction factor to the kinetic energy for general filling. We resolve the inconsistency in the existing literature for this problem as we find that our result for the half-filled case agrees with one of the three papers and attribute the discrepancy between them to the incorrect counting method and the assumption that the Gutzwiller approximation is equivalent to the mean-field slave-boson approach, which is although correct for the on-site Hubbard model, turns out not to be so in the present case. Compared with the exact diagonalization results, we show that the Gutzwiller method indeed offers a better solution than the slave-boson approach. As the second problem, we have studied the ground-state properties of paramagnetic LaMnO3 under hydrostatic pressure at room temperature. We apply the Gutzwiller method to an extended Hubbard model for spinless eg electrons on Mn3+ ion including all important ingredients such as cohesive energy as well as two main competing Coulomb and Jahn-Teller (JT) interactions. The plot of the energy of the paramagnetic LaMnO3 as a function of volume clearly confirms that 1) contrary to the existing accepted theoretical picture for vanishing lattice distortion as the metallic state emerges, the JT distortion survives even beyond the transition pressure into the metallic region and 2) the application of pressure leads to a structural phase separation and breaks the material into two blocks composed of domains of undistorted (metallic character) and distorted (insulating character) MnO6 octahedra; both of these findings have been already observed in experiments with no theoretical explanations. As the key unifying connection between both of these findings we suggest that the pressure-induced transition and the phase coexistence is indeed percolative. Finally, applying the idea of universality in percolation quantities near the threshold, we support our hypothesis by proposing a scaling law for the pressure-dependence of the resistance and use it as a best fit to recently-acquired experimental data. We find good agreement between our proposed model and the experimental results, confirming that the pressure-induced insulator-metal transition in LaMnO3 is indeed percolative.

This volume presents, for the very first time, an exhaustive collection of those modern numerical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and material science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciate consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.

A comprehensive introduction to state-of-the-art quantum Monte Carlo techniques for applications in strongly-interacting systems. Including variational wave functions, stochastic samplings, the variational technique, optimisation techniques, real-time dynamics and projection methods and recent developments on the continuum space. An extensive resource for students and researchers.

This book gathers a collection of reprints on the Hubbard Model. The major contributions to the subject since its origin are included, with the aim of providing all scientists working on the model and its applications with easy access to the relevant literature.The book is divided into five parts. The introductory part is concerned with the physical origin and motivations of the model, and contains a collection of mainly historical papers. The remaining four sections are intended to present a coherent scenario of the different approaches to the model solution: exact and rigorous statistical mechanics results; variational methods; perturbative approaches; numerical Quantum Monte Carlo and exact diagonalization studies. Among the applications special emphasis is given to high-Tc superconductivity. Each section is preceded by commentary notes from the editor.

Electronic structure and physical properties of strongly correlated materials containing elements with partially filled 3d, 4d, 4f and 5f electronic shells is analyzed by Dynamical Mean-Field Theory (DMFT). DMFT is the most universal and effective tool used for the theoretical investigation of electronic states with strong correlation effects. In the present book the basics of the method are given and its application to various material classes is shown. The book is aimed at a broad readership: theoretical physicists and experimentalists studying strongly correlated systems. It also serves as a handbook for students and all those who want to be acquainted with fast developing filed of condensed matter physics.

This book is a wide-ranging survey of the physics of out-of-equilibrium systems of correlated electrons, ranging from the theoretical, to the numerical, computational and experimental aspects. It starts from basic approaches to non-equilibrium physics, such as the mean-field approach, then proceeds to more advanced methods, such as dynamical mean-field theory and master equation approaches. Lastly, it offers a comprehensive overview of the latest advances in experimental investigations of complex quantum materials by means of ultrafast spectroscopy.