物质的量子相：多体系统中的纠缠和新材料的探寻

Recent years, many new phases of matter that possess tantalizing properties, like high-Tc superconductors, topological ordered phases, many-body localized states, and quantum critical states have been discovered, moreover, the behaviour of quantum systems away from equilibrium is now the subject of intense theoretical and experimental study in the context of ultra cold atom gases and optical lattices. It has become ever more clear that the behaviour of these phases of matter is dominated by quantum fluctuations, which in turn implies that the entanglement patterns in the wave-function are of fundamental importance. It turns out that the simpleamount of entanglementis not enough to characterize quantum phases or their critical behaviour. In a series of recent papers, we have shown that a much more refined description of entanglement in a many-body state can be obtained by Entanglement Spectrum Statistics(ESS). This project will continue to study the ESS, expect to provide a new theoretical tool to understand the notion of thermalization in closed quantum systems, quantum non-integrability, topological phases, MBL states, high-Tc superconductivity and quantum glasses. The main objects of study are: non-integrable and integrable models, MBL states and topological states. Moreover, since this approach is based on the wave-function and not on the Hamiltonian, it is possible to explore a much wider class of systems: open quantum systems, quantum circuit, time-dependent or driven quantum systems, quantum systems away from equilibrium. The study of ESS has a very strong potential for the understanding and discovering of quantum phases.

近年来许多具有诱人性质的新物质相被发现，例如高温超导体，拓扑有序相，多体局域态和量子临界态，而超冷原子气体和光晶格中远离平衡的量子系统的行为在理论和实验上都得到大量研究。人们已经越来越清楚的认识到，这些物质相的行为由量子涨落支配，波函数的纠缠模式具有基本的重要性。事实证明，简单的纠缠量对于刻划量子相或者它们的临界行为是不够的。我们的研究表明，纠缠谱统计对于多体态中纠缠的是一个更加精细的描述。本项目将继续研究纠缠谱统计，希望能提供一种新的理论工具来理解封闭量子系统的热化，量子不可积，拓扑相，多体局域态，高温超导和量子玻璃等现象。主要研究内容为：各类一维的可积和不可积模型，多体局域态，和拓扑态。此外，由于纠缠谱统计基于波函数而非哈密顿量，我们的研究对象还包括更广泛的领域，比如开放量子系统，量子线路，含时或驱动的量子系统，和远离平衡的量子系统。纠缠谱统计对于理解和发现新的量子相具有巨大的潜力。

物质的量子相与多体纠缠等是近年来理论物理中的热点问题。我们用2-Reny 纠缠熵作为工具，研究了一维量子多体系统自发对称性破缺基态的互信息。我们还研究了一维多体自旋模型基态附近时间平移对称性的破缺问题，并与量子时间晶体联系起来。我们研究了多体量子纠缠历史的理论与实验。我们研究了量子退火过程中拓扑序的热化问题，我们设计了量子电路，利用IBM量子云平台，实现了16个量子比特的多体Cluster态的制备。最后，我们研究了宏观系统的量子叠加态。这些研究对我们更深刻的理解量子多体相、多体纠缠与宏观量子效应有重要意义。