Strongly-entangled topological matter

这个项目将推进对一种名为拓扑物质的新型物质的理论理解，这种物质出现在强相互作用的量子系统中。通过进行数值模拟，该项目将研究拓扑物质的基本属性，如其几何和量子纠缠。这将为如何在双层石墨等材料中实现新的拓扑物质的实验提供反馈。拓扑学是数学的一个分支，描述对象的属性在局部扰动下不变。例如，足球和橄榄球是一样的，因为我们可以慢慢地将一个球伸展到另一个球中。奇怪的是，在某些半导体材料(如用于制造晶体管和太阳能电池的材料)中，存在着对局部扰动也不敏感的物质相。这种拓扑物质与普通物质(如水或冰)非常不同，因为它代表了许多量子粒子相互作用时出现的集体状态，类似于超流体和超导体。拓扑物质形成了现代凝聚态物理学中一个非常活跃的领域，至少有三个原因。首先，从20世纪80年代分数量子霍尔效应的最初发现开始，拓扑物质已经在许多美丽的实验中被看到。其次，拓扑物质对理论物理来说是一个重大挑战，因为它不能用基于对称破缺的传统固态理论来解释。第三，拓扑相具有非常丰富和意想不到的性质，例如，它们的低能激发表现为比粒子物理标准模型更一般的“准粒子”(即它们既不是玻色子也不是费米子)。最近发现的一种这样的准粒子--马约拉纳费米子--引起了公众的极大关注，目前的研究重点是利用马约拉纳的力量进行量子计算。因此，拓扑物质可能会在未来的量子技术中发挥重要作用。这个项目将促进对强相互作用粒子系统中拓扑物质的理解，在这个系统中，许多基本问题仍然悬而未决。该项目将研究几何在拓扑物质中的作用，拓扑物质决定了它们的弹性和热性质。此外，该项目将研究拓扑物质中的量子关联(“纠缠”)，目的是了解拓扑秩序如何能够在高温下生存。这将是一项重要的实践进步，因为目前大多数拓扑物质只能在低温条件下实现。最后，该项目将与寻求在新材料中实现拓扑物质的实验建立密切联系。通过开发和应用新的数值算法，该项目将识别相互作用驱动的拓扑现象，这些现象可以在双层石墨烯中通过实验获得，特别是拥有Majorana费米子或甚至更奇异的“准费米”准粒子的相。

This project will advance the theoretical understanding of the new type of matter called topological matter, which emerges in strongly-interacting quantum systems. By performing numerical simulations, the project will investigate fundamental properties of topological matter, such as its geometry and quantum entanglement. This will provide feedback to experiments on how to realise new topological matter in materials like bilayer graphene.Topology is a branch of mathematics that describes properties of objects which do not change under local perturbations. For example, a soccer ball is the same as a rugby ball because we can slowly stretch one into the other. Curiously, in certain semiconductor materials (like the ones used to build transistors and solar cells) there are phases of matter which are also insensitive to local perturbations. This topological matter is very different from ordinary matter (like water or ice) because it represents a collective state that emerges when many quantum particles interact, similar to superfluids and superconductors. Topological matter forms a very active field of modern condensed matter physics, for at least three reasons. First, topological matter has been seen in many beautiful experiments, starting with the original discovery of the fractional quantum Hall effect in the 1980s. Second, topological matter represents a major challenge for theoretical physics, because it cannot be explained by traditional solid state theories based on "symmetry breaking". Third, topological phases have very rich and unexpected properties, for example their low-energy excitations behave as "quasiparticles" which are more general than the Standard Model of particle physics (i.e., they are neither bosons nor fermions). Recent discovery of one such quasiparticle - the "Majorana fermion" - has attracted much public attention, and current research focuses on harnessing the power of the Majoranas to perform quantum computing. Thus, topological matter may have an important role to play in future quantum technologies. This project will advance the understanding of topological matter in the systems of strongly interacting particles, where many fundamental problems remain open. The project will investigate the role of geometry in topological matter, which determines their elastic and thermal properties. Furthermore, the project will investigate quantum correlations ("entanglement") in topological matter, with the goal of understanding how topological order could be enabled to survive at high temperatures. This would represent an important practical advance as most of topological matter is currently realised only at cryogenic conditions. Finally, the project will establish close connection to experiments that seek to realise topological matter in new materials. By developing and applying new numerical algorithms, the project will identify interaction-driven topological phenomena that can be experimentally accessed in bilayer graphene, in particular the phases that host the Majorana fermions or even more exotic "parafermion" quasiparticles.