The Gutzwiller variational method for strongly correlated systems
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] 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.
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