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Quantum Entanglement and Dynamics in Lattice Systems

晶格系统中的量子纠缠和动力学

基本信息

批准号：
1918207
负责人：
Israel Klich
金额：
$ 45万
依托单位：
University of Virginia Main Campus
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-06-01 至 2023-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1918207&HistoricalAwards=false
关键词：
Quantum Entanglement Dynamics Lattice Systems

项目摘要

NONTECHNICAL SUMMARYThis award supports fundamental theoretical research and education aimed at advancing our grasp of quantum aspects of condensed matter theory at low dimensions. The major fundamental difficulty in describing and theoretically representing quantum many-body systems is the vast number of parameters required. The number of such parameters increases exponentially with the number of constituents of a system, and thus quickly becomes intractable for numerical computations, even for small quantum systems. Thus, efficient descriptions of quantum systems are of fundamental importance to our understanding of complex systems and of their applications. In this project, the PI will study a new representation for certain quantum systems that is exact and efficient. Another front of the research is the development of models of quantum systems that efficiently describe their dynamics, for example quantum detectors under the influence of measurements and external disturbances. The detailed understanding of such dynamics may find a crucial role in the development of a host of new experimental diagnostic tools, and of platforms for quantum computing.The project will require the use and development of new theoretical tools in the arsenal of theoretical physics of many-body quantum states. Also, in tandem with the research, the project will involve the training of graduate students in cutting-edge methods of theoretical physics, which are vital for a scientific career but also form a core of ideas that often find new uses in industry.TECHNICAL SUMMARYThis award supports theoretical research and education to advance our grasp of quantum aspects of condensed matter theory at low dimensions through the study of entanglement, dynamics, and fluctuations in many-body states. There are three main topics of study:The first topic is a study of the interplay of locality and entanglement and its relation to variational methods like tensor network states. The PI will focus on recently discovered Hamiltonians that exhibit highly entangled ground states and new phase transitions, and unusual dynamical scaling properties.The second topic will deal with a set of quantum nonequilibrium problems, a topic of current interest due to advancement in theory and experiment. Theory lags significantly behind experimental abilities primarily due to the inability to effectively simulate many-body dynamics. Via a numerical framework based on closed hierarchies of equations, the PI will study nonequilibrium current generation, effects of the motion of detectors and sources in a Fermi sea, quantum wakes, and role of the interplay between disorder and measurements.In a third topic, the PI will investigate a new class of boson impurity models that can be mapped into certain photonic cluster states, with particular emphasis on relating these states to ground states of interesting physical disordered systems that may ultimately be amenable to quantum simulation.The methods and approaches employed and developed will allow for a fruitful exchange of ideas between researchers in condensed matter, quantum information, high-energy physics, and in mathematics. Nonequilibrium quantum physics plays a role in a wide swath of applications from fundamental physics understanding to the development of devices. Finally, an essential component of the project is that it will provide opportunities for the training of new researchers, whose development as scientists is a vital goal of the proposed activity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术总结该奖项支持基础理论研究和教育，旨在提高我们对低维凝聚态理论量子方面的理解。描述和理论表示量子多体系统的主要基本困难是所需的大量参数。这样的参数的数量随着系统的成分数量呈指数增长，因此对于数值计算来说很快变得棘手，即使是对于小的量子系统。因此，量子系统的有效描述对于我们理解复杂系统及其应用至关重要。在这个项目中，PI将研究某些量子系统的新表示，这是精确和有效的。研究的另一个前沿是开发有效描述其动态的量子系统模型，例如在测量和外部干扰影响下的量子探测器。对这种动力学的详细理解可能会在开发一系列新的实验诊断工具和量子计算平台方面发挥关键作用。该项目将需要使用和开发多体量子态理论物理武器库中的新理论工具。此外，在研究的同时，该项目还将涉及对研究生进行理论物理前沿方法的培训，这些方法对科学事业至关重要，但也构成了经常在工业中找到新用途的思想核心。技术总结该奖项支持理论研究和教育，通过对纠缠，动力学，以及多体状态的涨落主要有三个研究主题：第一个主题是研究局域性和纠缠的相互作用及其与张量网络态等变分方法的关系。PI将专注于最近发现的具有高度纠缠基态和新相变的哈密顿量，以及不寻常的动力学标度特性。第二个主题将处理一系列量子非平衡问题，这是由于理论和实验的进步而引起的当前兴趣的主题。理论明显落后于实验能力，主要是由于无法有效地模拟多体动力学。通过一个基于封闭方程组的数值框架，PI将研究非平衡电流的产生，费米海中探测器和源运动的影响，量子尾流，以及无序和测量之间相互作用的作用。在第三个主题中，PI将研究一类新的玻色子杂质模型，这些模型可以映射到某些光子团簇态，特别强调将这些状态与有趣的物理无序系统的基态联系起来，这些系统最终可能适合量子模拟。所采用和开发的方法和途径将使凝聚态，量子信息，高能物理和数学领域的研究人员之间进行富有成效的思想交流。非平衡量子物理学在从基础物理学理解到设备开发的广泛应用中发挥着作用。最后，该项目的一个重要组成部分是，它将为新的研究人员提供培训机会，他们作为科学家的发展是拟议活动的一个重要目标。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。