Electronic structure and dynamics in quasi-disordered systems, from quasiperiodic potentials to quantum spin ice

凝聚态物理传统上关注的是生活在晶格上的长程有序系统，这是该领域的中心工具，如布洛赫定理，适用的领域。安德森和莫特的工作改变了这一图景，他们意识到无序和强相互作用可以导致局域化，这与布洛赫关于扩展电子本征态的定理图景相矛盾。自那以后，对无序、强相互作用和局域化之间的联系的理解导致了凝聚态物理学的重要发展，最近发现了多体定域化。我的项目关注的是“准无序”系统的丰富物理学，也就是物质在完美有序和完全无序之间的相态。我的重点是两个例子：1.准晶实际上是长程有序的；然而，与晶体不同的是，这种有序是非周期的，因此布洛赫定理不适用。因此，它们成为周期晶体和无序系统之间的中间地带，具有独特的局域化和拓扑性质。我研究了一维和二维准晶的Anderson局域化转变，这些准晶显示了新的类型的临界行为。受挫的磁体有大量简并的基态：尽管这些基态是无序的，但这种相互作用的形式导致了微妙和不寻常的长程关联无序和独特的自旋液体相。特别是，我研究了新的方法来理解自旋冰系统的自旋动力学和电子结构。

Condensed matter physics is traditionally concerned with long-range ordered systems living on crystalline lattices, and this is the domain where the central tools of the field, such as Bloch's theorem, are applicable. This picture was changed by the work of Anderson and Mott who realised that disorder and strong interactions can result in localisation, contradicting the Bloch's theorem picture of extended electronic eigenstates. Understanding the connection between disorder, strong interactions, and localisation has since led to important developments in condensed matter physics, most recently to the discovery of many-body localisation. My project is concerned with the rich physics of "quasi-disordered" systems, that is, phases of matter between the limits of perfect order and complete, uncorrelated disorder. I focus on two examples:1. Quasicrystals are, in fact, long-range ordered; unlike crystals, however, this order is aperiodic, and so Bloch's theorem does not apply. As such, they emerge as a middle ground between periodic crystals and disordered systems, with unique localisation and topological properties. I investigate Anderson localisation transitions of one- and two-dimensional quasicrystals which display novel kinds of critical behaviour.2. Frustrated magnets have massively degenerate ground states: although these are disordered, the form of interactions result in subtle and unusual long-range correlated disorder and unique spin liquid phases. In particular, I investigate novel methods to understand the spin dynamics and electronic structure of spin ice systems.