Exotic phases in strongly correlated parafermion chains

Quantum computers will be the next revolution in computer science. Molecular simulations, medicine research, route optimalisation and material science are just a few examples that will greatly benefit from this new form of computation. Currently, the biggest challenge arises in the instability of the qubits, the smallest building block of the quantum computer. External interference or interactions can knock these qubits off balance, causing a loss of information. This thesis contributes to the theoretical physics understanding of a new qubit candidate: the topological qubit. Contrary to an ordinary computer, a quantum computer does many computations simultaneously. The fact that qubits can be in 2 phases at once, makes this possible. Qubits are not a [0] OR [1], like a usual bit, but rather a combination: [0] + [1]. This combination is fragile, disturbances can break this sum, resulting in a [0] OR [1]. Topological qubits are protected against these kind of decay processes, because the [0] and [1] are spatially widely separated. This eliminates the sensitivity to interference. This thesis is dedicated to the study of parafermions, one particular type of topological qubit or topological system. These exotic parafermions are particles that can only appear in 1- or 2-dimensional materials. The various chapters discuss the conditions required for the combination state to survive in the context of parafermions. Also the effect of specific distortions is shown to have little effect on qubit state.