Quantum thermalisation and many-body localisation

“量子多体系统是如何热化的？它们能不能达到热平衡？热力学定律和量子力学定律是相容的吗？尽管人们已经知道量子力学的基本定律100多年了，但这个基本问题仍然没有得到彻底的回答。近年来，在理解热化及其分解方面取得了重大进展。多体定位（MBL）。越来越明显的是，量子信息的传播在描述这些现象中起着至关重要的作用。此外，还介绍了近年来在固态系统量子控制方面的实验进展，（NV中心，量子点）和合成量子系统（冷原子，捕获的离子）已经允许在实验室中探索这些问题。这个项目的目的是研究热化和许多-通过揭示本征态的纠缠结构和多体系统动力学机制，纠缠候选人将使用精确对角化和多体微扰理论来计算纠缠度，如负性和互信息。利用量子信息论中纠缠单偶的思想，提取多体纠缠的特征长度尺度，描述两相物质的本征态及其动力学行为。这将对量子模拟器中未来的动力学实验产生潜在的影响。"

"How do quantum many-body systems thermalise? Can they ever fail to reach thermal equilibrium? Are the laws of thermodynamics and quantum mechanics compatible with each other? In spite of knowing the basic laws of quantum mechanics for more than 100 years, this basic question is yet to be thoroughly answered. In recent years there has been significant progress in understanding both thermalisation and its breakdown, a.k.a. many-body localisation (MBL). It is increasingly evident that the propagation of quantum information plays a crucial role in describing these phenomena. Furthermore, recent experimental progress in quantum control of solid state systems (NV centres, quantum dots) and synthetic quantum systems (cold atoms, trapped ions) has allowed exploration of these questions in the laboratory.This project will aim to study the properties of thermalisation and many-body localisation in spin chains and toy models by shedding new light on the entanglement structure of eigenstates and regimes of dynamics of multipartite entanglement. The candidate will use exact diagonalisation and many-bodyperturbation theory for calculating measures of entanglement such as negativity and mutual information. By using ideas of monogamy of entanglement from quantum information theory, a characteristic length scale for multipartite entanglement will be extracted to characterise the eigenstates and their dynamics in the two phase of matter. This will have potential implications for future dynamics experiments in quantum simulators."