Overview

The thesis is a collection of three topics connected together by the common themes of strong interactions, magnetism and quantum phases, such as the Aharonov-Bohm or Berry phase. The first part of the present dissertation discusses the possibility of examining microscopic origins of magnetism in strongly interacting systems by exploiting the setting of ultra-cold atomic gases in optical lattices. We discuss signatures of correlation in the trap, and propose an experiment to measure the phase diagram of itinerant magnetism directly. The second part focuses on the exotic phase of matter exhibiting the Fractional Quantum Hall Effect, which emerges when interacting particles are placed in a very strong magnetic field. We propose a trial ground state wave-function and prove that it is the unique highest density ground state of a well-motivated pseudo-potential Hamiltonian. The exchange statistics of quasiparticles are shown to be exotic, and overlaps with results of exact diagonalization are also discussed. The final part of the thesis studies frustrated magnetic systems, in which competing forces cannot not be satisfied simultaneously, doped with electrons. The interplay of frustration and itinerant behavior generates Berry phases associated with charge transport. We study the effects of these phases on electronic behavior, as well as the effect electrons have on the underlying magnetic textures. In the quasi-classical limit, we conjecture a field-driven metal-insulator transition, and discuss persistent currents arising in ground states selected by the presence of charge. In the quantum regime we derive the full Hamiltonian and discuss small fluctuations about the classical results.

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9781243603562

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