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

本计画旨在研究物质的拓扑相，并将其应用于拓扑量子计算。特别是，它将检查拓扑的“边缘零”模式的一维马约拉纳费米子和parafermion链，以及是否整个本征态谱的简并性，他们诱导被打破时，相互作用或无序添加到系统。它将研究这种简并和多体局域化之间的关系，这提供了本征态相变的另一个例子。特别是，我专注于'强边零'模式在马约拉纳费米子和parafermion链，以及它们是否可以生存在相互作用，不可积系统，如当四个费米子相互作用项包括在哈密顿量。我调查这两个明确的（计算机辅助）分析计算的强零模式微扰理论，并通过数值研究的具体哈密顿。该项目福尔斯EPSRC的研究领域“凝聚态物质：电子结构”，尽管它也与“凝聚态物质：磁性和磁性材料”有很大的重叠，两者都属于“物理科学”主题。

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.