Free-particle descriptions of topological quantum matter and many-body localisation

自由粒子的概念是理论物理学的核心。这个简单的概念使我们能够描述自然界中各种各样的系统：例如，我们将原子解释为自由电子的集合，将电磁辐射解释为一组自由谐振子。但在真实的世界中，粒子之间也会相互作用。相互作用在量子系统中具有特别显著的影响，它们导致长距离相关和量子纠缠。这使得量子多粒子系统的理论描述非常具有挑战性。与此同时，人们越来越有兴趣将交互作为一种可以彻底改变技术的资源。现代技术一直基于量子材料，如半导体，超导体和磁铁，这些材料构成了激光器，晶体管，计算机等的构建模块，近年来，通过利用量子物理学的全部力量，使这些设备变得更加强大，这将通过利用量子关联和纠缠来实现。因此，在现阶段，有一个迫切的理论和实践需要了解和操纵的量子系统中的相互作用的影响，这个建议将研究两个物理系统的当前利益的相互作用导致新的物理现象：（1）拓扑相的物质，其中包括马约拉纳和parafermion自旋链，自旋液体和分数量子霍尔态。这些相是由于相互作用的“非微扰”效应而形成的，并且不能被描述为自由电子的集合。这使它们具有独特的性质，例如在任意但足够弱的扰动下的鲁棒性。由于这种特殊的刚性，拓扑量子物质正被用作更强大的量子技术的基石，旨在适应环境扰动。(2)量子多粒子系统的非平衡动力学和热化。典型的量子系统是遍历的：它们很快达到热平衡，因为它们的组成粒子之间的相互作用很快消除了系统初始条件的记忆。然而，最近关于“多体局域化”的工作表明，存在大量强无序、相互作用的量子系统，它们无法达到热平衡。因此，这些系统是非遍历的，这意味着其中的量子效应可以持续非常长的时间，从而为量子技术提供了另一种保护途径。在这个提议中，我们将发展一种新的方法来描述强关联现象中的相互作用效应，包括物质的拓扑相和多体局域化。我们将使用最先进的数值模拟推进随机环境中多体系统的建模。我们的理论研究的拓扑结构和多体定位在量子物质的影响将影响几个实验冷原子，被困离子，固体中的缺陷等，最后，我们将探讨实现相位与拓扑秩序在随机环境中的可能性，并提出计划量子信息存储和处理具有增强的稳定性对thermalisation。

The notion of a free particle is at the heart of theoretical physics. This simple notion allows us to describe a wide variety of systems in nature: for example, we explain atoms as collections of free electrons, and electromagnetic radiation as a set of free harmonic oscillators. But in real world, particles also interact with one another. Interactions have particularly striking effects in quantum systems, where they lead to long-range correlations and quantum entanglement. This makes the theoretical description of quantum many-particle systems very challenging. At the same time, there is growing interest in using interactions as a resource that could revolutionise technology. Modern technology has been based on quantum materials such as semiconductors, superconductors and magnets, which form the building blocks of lasers, transistors, computers, etc. In recent years, there has been a shift towards making such devices more powerful by exploiting the full power of quantum physics, which will be achieved by utilising quantum correlations and entanglement. Thus, at this stage, there is a compelling theoretical and practical need to understand and manipulate the effects of interactions in quantum systems.This proposal will investigate two physical systems of current interest where interactions lead to novel physical phenomena: (1) Topological phases of matter, which include Majorana and parafermion spin chains, spin liquids and fractional quantum Hall states. These phases form as a result of "non-perturbative" effects of interactions, and cannot be described as a collection of free electrons. This gives them unique properties such as robustness under arbitrary, but sufficiently weak, perturbations. Because of this special rigidity, topological quantum matter is being used as a building block of more robust quantum technologies, designed to be resilient to environmental perturbations.(2) Non-equilibrium dynamics and thermalisation in quantum many-particle systems. Typical quantum systems are ergodic: they quickly reach thermal equilibrium because the interactions between their constituent particles quickly erase the memory of the system's initial condition. However, recent work on "many-body localisation" shows that there exist large classes of strongly-disordered, interacting quantum systems which fail to reach thermal equilibrium. These systems are thus non-ergodic, which means that quantum effects in them can persist for unusually long times, thus providing another route of protection for quantum technology.In this proposal we will develop a new approach to describe interaction effects in strongly-correlated phenomena including topological phases of matter and many-body localisation. We will advance the modelling of many-body systems in random environments using state-of-the-art numerical simulations. Our theoretical investigation on the effects of topology and many-body localisation in quantum matter will impact several experiments on cold atoms, trapped ions, defects in solids, etc. Finally, we will explore the possibility of realising phases with topological order in random environments, and propose schemes for quantum information storage and processing with an enhanced stability against thermalisation.