The Quantum Hall Problem In Lattices
This thesis represents a body of work investigating the physics of strongly interacting quantum particles, confined to a two-dimensional plane in a nontrivial vector potential (such as a transverse magnetic field), commonly referred to as quantum Hall physics. The result which anchors these studies is my discovery, reported in 2010 (PRL 105, 215303), of a lattice model in which there is a degenerate manifold of single-particle states, with wavefunctions matching those of the lowest Landau level of continuum particles, providing a bridge between continuum and lattice physics. Within this model anyonic states are robust and thus amenable to observation. Building on this result, I numerically demonstrate the braiding of anyons in many-body quantum Hall states of bosons, confirming their anyonic statistics. I also study the equation of state of quantum Hall bosons for various flux densities and choices of hopping parameters, with the goal of quantifying the effects of finite temperature and examining the feasibility of observing these states in a system of cold atoms. I then propose a new architecture for superconducting qubits, where flux states of circulating current combined with superconducting transformers and tuned voltage offsets mimic the physics of charged particles in a magnetic field, allowing boson quantum Hall physics to be studied in an environment free of charge noise. Finally, I review the work presented here and speculate on its possible applications to topological quantum computing.
Quantum Hall Physics; Quantum Simulation; Topological Quantum Computing
Shen, Kyle M.; Leclair, Andre Roger
Ph. D., Physics
Doctor of Philosophy
dissertation or thesis