Doctoral Dissertations

Date of Award


Degree Type


Degree Name

Doctor of Philosophy



Major Professor

Elbio Dagotto

Committee Members

Adriana Moreo, Steven Johnston, David Mandrus


In this thesis, we study the interplay of Hubbard U correlation and topological effects in two different bipartite lattices: the dice and the Lieb lattices. Both these lattices are unique as they contain a flat energy band at E = 0, even in the absence of Coulombic interaction. When interactions are introduced both these lattices display an unexpected multitude of topological phases in our U -λ phase diagram, where λ is the spin-orbit coupling strength. We also study ribbons of the dice lattice and observed that they qualitative display all properties of their two-dimensional counterpart. This includes flat bands near the Fermi level, edge currents when open boundary conditions are used, two chiral edge modes (because the planar Chern number is 2), and a nonzero Hall conductance. This opens the possibility of studies of these systems using powerful techniques such as the density matrix renormalization group that work well for ribbons. Finally, we study a multi-orbital Hubbard model for two and three orbitals per site on a two-site cluster and mapped our results into a higher-order effective spin Heisenberg model to know the limitations in the value of the couplings that can be used with those effective models. Numerical techniques, such as the Hartree-Fock approximation, Lanczos and density matrix renormalization group, were used to carry out these studies at half-filling.

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