Quantum Entanglement and Dynamics in Lattice Systems

该奖项支持基础理论研究和教育，旨在推进我们对低维凝聚态理论量子方面的掌握。描述和从理论上表示量子多体系统的主要基本困难是所需的大量参数。这些参数的数量随着系统组成部分的数量呈指数增长，因此对于数值计算来说很快变得难以处理，即使对于小量子系统也是如此。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精确和高效的新表示。研究的另一个前沿是发展量子系统模型，有效地描述它们的动力学，例如量子探测器在测量和外部干扰的影响下。对这种动力学的详细理解可能会在一系列新的实验诊断工具和量子计算平台的开发中发挥关键作用。该项目将需要在多体量子态理论物理的武器库中使用和开发新的理论工具。此外，在研究的同时，该项目还将涉及对研究生的理论物理前沿方法的培训，这对科学事业至关重要，但也形成了经常在工业中找到新用途的核心思想。该奖项支持理论研究和教育，通过研究多体态的纠缠、动力学和波动，推进我们对低维凝聚态理论量子方面的掌握。有三个主要的研究主题：第一个主题是研究局部性和纠缠的相互作用及其与张量网络状态等变分方法的关系。PI将重点关注最近发现的哈密顿量，这些哈密顿量表现出高度纠缠的基态和新的相变，以及不寻常的动态缩放特性。第二个主题将处理一组量子非平衡问题，由于理论和实验的进步，这是一个当前感兴趣的主题。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。通过一个基于封闭层次方程的数值框架，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状态，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用于量子模拟。所采用和发展的方法和途径将使凝聚态物质、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理解到设备开发的广泛应用中发挥着重要作用。最后，该项目的一个重要组成部分是，它将为培训新的研究人员提供机会，使他们发展成为科学家是拟议活动的一个重要目标。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.