Quantum theory of strong interactions in low dimensional systems

任意子作为强相关系统的某些相的激发态出现，其缩影是分数量子霍尔态。这类准粒子的性质与其他粒子不同（即既不是费米子也不是玻色子），对拓扑量子计算的发展具有重要意义。在这个未来的架构中，量子比特是由系统的非局域特性编码的，因此它们对局域噪声和退相干具有鲁棒性，并且可以通过编织任何电子激励来操作。一些范德华二维材料，如RuCl3，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，普遍缺乏表现出这些奇异特征的物质相。鉴于对量子技术应用的兴趣，从基础角度研究如何产生承载（可能可控的）任意激振的奇异量子相是至关重要的。最近，该小组已经证明扭曲的基塔耶夫模型（一种捕捉量子自旋液体特征的真实材料的粗略近似）可以展示出前所未有的物质相。特别是，它们可以以类似于kagome的模式显示任意子的定位。在这个项目中，我们想超越现有的模型，包括真实材料中存在的特征，特别是超越基塔耶夫自旋相互作用。我们的目标是通过分析和数值技术的结合来做到这一点，包括通过变分方法这些相互作用的作用。因此，学生将推导出描述所研究系统中由于超基塔耶夫相互作用而产生的准粒子运动的有效模型。然后，我们将求解得到的模型并找到相变点，并改进我们的扭曲量子自旋-液体双分子层的结果。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.