First principles quantum Monte Carlo study of correlated electronic systems

The many-body correlation between electrons is the origin of many fascinating phenomena in condensed matter systems, such as high temperature superconductivity, superfluidity, fractional quantum Hall effect, and Mott insulator. Strongly correlated systems have been an important subject of condensed matter physics for several decades, especially after the discovery of high temperature cuprate superconductors. In this thesis, we apply first principles quantum Monte Carlo (QMC) method to several representative systems to study the electron correlations in transition metal oxides (vanadium dioxide) and low dimensional electronic systems (graphene and graphene-like two dimensional systems). Vanadium dioxide (VO2) is a paradigmatic example of a strongly correlated system that undergoes a metal-insulator transition at a structural phase transition. To date, this transition has necessitated significant post-hoc adjustments to theory in order to be described properly. We apply first principles quantum Monte Carlo (QMC) to study the structural dependence of the properties of VO2. Using this technique, we simulate the interactions between electrons explicitly, which allows for the metal-insulator transition to naturally emerge, importantly without ad-hoc adjustments. The QMC calculations show that the structural transition directly causes the metal-insulator transition and a change in the coupling of vanadium spins. This change in the spin coupling results in a prediction of a momentum-independent magnetic excitation in the insulating state. While two-body correlations are important to set the stage for this transition, they do not change significantly when VO2 becomes an insulator. These results show that it is now possible to account for electron correlations in a quantitatively accurate way that is also specific to materials. Electron correlation in graphene is unique because of the interplay of the Dirac cone dispersion of pi electrons with long range Coulomb interaction. The random phase approximation predicts no metallic screening at long distances and low energies because of the zero density of states at Fermi level. It is thus interesting to see how screening takes place in graphene at different length scales. We addressed this problem by computing the structure factor S(q) and S(q, ω) of freestanding graphene using ab initio fixed-node diffusion Monte Carlo and the random phase approximation. The X-ray measured structure factor is reproduced very accurately using both techniques, provided that sigma-bonding electrons are included in the simulations. Strong dielectric screening from sigma electrons are observed, which redshifts the pi plasmons resonance frequency at long distance and reduces the effective interactions between pi electrons at short distance. The short distance screening makes suspended graphene a weakly correlated semimetal which otherwise would be an insulator. The third piece of works is dedicated to studying the low energy excitation of many-body systems using extended Koopmans' theorem (EKT). The EKT provides a straight forward way to compute charge excitation spectra, such as ionization potentials, electron affinities from any level of theory. We implemented the EKT within the QMC framework, and performed systematic benchmark studies of ionization potentials of the second- and third-row atoms, and closed- and open-shell molecules. We also applied it to compute the quasiparticle band structure of solids (graphene). For complex correlated systems, identifying relevant low energy physics degrees of freedom is extremely important to understanding the system's collective behavior at different length scales. In this sense, bridging the realistic systems to lower energy effective lattice models that involve fewer but important degrees of freedom is significant to understanding correlated systems. We have formulated three ab initio density matrix based downfolding (AIDMD) methods to downfold the ab initio systems into effective lattice models. We have demonstrated the successfulness of these methods by applying them to molecules (H2) and periodic systems (hydrogen chain and graphene)