Strong edge zero modes in integrable and non-integrable models and their relation to long coherence times of edge spins

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This project aims to research topological phases of matter with eventual view to application in topological quantum computing. In particular, it will examine the topological 'edge zero' modes of 1D Majorana fermion and parafermion chains, and whether the degeneracy of the entire eigenstate spectrum they induce is broken when interactions or disorder are added to system. It will investigate the relationship between this degeneracy and many-body localisation, which provides another example of an eigenstate phase transition. In particular, I am focussing on 'strong edge zero' modes in Majorana fermion and parafermion chains, and whether they can survive in interacting, non-integrable systems, such as when four fermion interaction terms are included in the Hamiltonian. I am investigating this both by explicit (computer-aided) analytical calculation of the strong zero modes in perturbation theory, and by numerical investigation of the specific Hamiltonians involved. The project falls under the EPSRC research area 'Condensed matter: electronic structure', although it also has significant overlap with 'Condensed matter: magnetism and magnetic materials', both in the 'Physical Sciences' theme.