Quantum theory of strong interactions in low dimensional systems

任意子作为强关联系统的某些相的激发而出现，其缩影是分数量子霍尔态。这种准粒子的行为与自然界中的其他粒子不同（即它们既不是费米子也不是玻色子），这对拓扑量子计算的发展很有意义。在这种未来主义的架构中，量子比特由系统的非局域性质编码，因此它们对局域噪声和退相干具有鲁棒性，并且它们可以通过编织任意子激发来操作。一些货车德瓦尔斯二维材料，如RuCl 3，最近被证明具有量子自旋液相，其激发也可以表现为任意子。然而，证据仍然存在争议。此外，一般来说，表现出这些奇异特征的物质相很少。考虑到量子技术应用的兴趣，从基本的角度研究如何产生具有（可能可控的）任意子激发的奇异量子相是关键。最近，该小组已经证明，扭曲的Kitaev模型（一种粗略的近似真实的材料，捕获了一些量子自旋液体特征）可以表现出前所未有的物质相。在这个项目中，我们希望超越现有的模型，包括存在于真实的材料中的特征，特别是超越Kitaev自旋相互作用。我们的目标是这样做的分析和数值技术相结合，包括通过变分方法这些相互作用的作用。因此，学生将推导出有效的模型，描述由于超越Kitaev相互作用所研究的系统中准粒子的运动。然后，我们将解决由此产生的模型，并找到相变点，并改善我们的扭曲量子自旋液体双层的结果。因此，该项目位于量子材料设计和（由于其可能的应用）量子技术之间的交叉点。

Anyons emerge as excitations of certain phases of strongly-correlated systems, the epitome of which is the fractional quantum Hall state. Such quasiparticles, which behave as no other particle in nature (i.e. they are neither fermions nor bosons) are of interest for development of topological quantum computation. In this futuristic architecture, qubit are encoded by non-local properties of the system, thus they are robust to local noise and decoherence, and they can be operated upon by braiding anyonic excitations.Some van der Waals 2D materials, such as RuCl3, have recently been shown to host quantum spin liquid phases whose excitations can also behave as anyons. However, evidence remains controversial. Furthermore, there is a general paucity of phases of matter that exhibit these exotic features. Given the interest in quantum technology applications, it is pivotal to investigate from a fundamental perspective how to generate exotic quantum phases hosting (possibly controllable) anyonic excitations on-demand. Recently, the group has shown that twisted Kitaev models (a crude approximation to real materials that capture some of the quantum spin liquid features) can exhibit unprecedented phases of matter. In particular, they can exhibit localisation of anyons in emergent Kagome-like pattern.In this project we want to go beyond the existing model and include features existing in real materials, in particular beyond-Kitaev spin interactions. We aim at doing this with a combination of analytical and numerical techniques, including the role of these interactions via variational methods. The student will therefore derive effective models describing the motion of quasiparticles in the systems under study due to beyond-Kitaev interactions. We will then solve the resulting models and find phase transition points and improve our results of twisted quantum-spin-liquid bilayers. The project thus sits at the intersection between quantum material design and (because of its possible applications) quantum technology.