Campus Only Senior Thesis
Bachelor of Arts
The Hubbard model is a prototypical model describing interacting electrons. Despite its simple form, the Hubbard model is not integrable, and the complete phase diagram remains unresolved. In this thesis, we consider the Hubbard model for two systems and derive suitable effective spin-spin Hamiltonians from it. First, we explore the spin Hamiltonian on a bilayer square lattice and analyze the ground state and dynamical properties. We consider an isotropic spin model with first and second neighbor Heisenberg interaction and determine the variational phase diagram. Allowing for a quantum entanglement on the bonds connecting the top and bottom layer of the lattice, we investigate a phase transition between magnetic and dimerized singlet phases. To describe the dynamics of the triplet excitations in the magnetically disordered dimer-singlet state, we introduce bond-wave formalism as a generalization of spin waves. We derive the equations of motions for the triplets and obtained the excitation spectrum using the Bogoliubov transformation. In the second project, we go beyond entangling only two sites. We consider the Hubbard model for a small cluster of 5 sites and classify the possible states corresponding to half-filling according to their magnetic properties. We show that for a wide range of parameter values, the 5-site tetrapod has a spin 32 ground state. The tetrapod is a generalization of the triangulene that is an effective spin-1 object. We use the tetrapods as building blocks of artificial spin systems exhibiting fascinating entangled nonmagnetic states that can realize novel platforms for quantum computation.
Benjamin, Claire, "Dimerization and Entangled Phases in Quantum Spin Systems" (2023). Scripps Senior Theses. 2050.
This thesis is restricted to the Claremont Colleges current faculty, students, and staff.