Strong edge zero modes in integrable and non-integrable models and their relation to long coherence times of edge spins
Lead Research Organisation:
University of Oxford
Department Name: Oxford Physics
Abstract
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.
Organisations
People |
ORCID iD |
| Paul Fendley (Primary Supervisor) | |
| Jack Kemp (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509711/1 | 01/10/2016 | 30/09/2021 | |||
| 1963205 | Studentship | EP/N509711/1 | 01/10/2015 | 30/09/2019 | Jack Kemp |
| Description | The research as part of my PhD funded through the grant has focussed on 'strong edge zero modes', excitations which live at the edge of certain quantum systems with a long coherence time, which could be used to make stable qubits for quantum computing. In particular, it has found that, and explained why, a much wider set of systems than naively expected possess 'almost' strong zero modes, which display exponentially long but not infinite coherence times, and which could still be useful for quantum computing. |
| Exploitation Route | Fundamental questions behind strong zero modes and their relationship to other fundamental properties such as integrability still need to be pursued, building on this research. Also, as alluded to above, several experimental tests for strong zero modes have been proposed and these could ultimately be of use in quantum computing. |
| Sectors | Other |