Topology in many-body quantum systems in and out of equilibrium

处于平衡状态和非平衡状态的多体量子系统中的拓扑

• 批准号: 2300172
• 负责人: Lukasz Fidkowski
• 金额: $ 38.1万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-01-01 至 2026-12-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2300172&HistoricalAwards=false
• 关键词: Topology; many; body; quantum; systems

NON-TECHNICAL SUMMARY:This award supports theoretical and computational research and education to investigate the behavior of quantum systems with many particles, such as electrons in a crystalline solid. The large number of electrons and their inherent quantum mechanical nature can act in concert leading to new states of matter. Among these are superconductors, which can conduct electricity with zero resistance, and the quantum Hall states, in which a strong magnetic field causes electrons confined to two dimensions to execute tight circular orbits, thereby forcing net electrical current flow to thei edges of the system. The goal of the PI’s work is to combine tools from theoretical condensed matter and quantum information theory to gain an understanding of these states of quantum matter. In the last few years, quantum computing has motivated significant progress in condensed matter theory. Quantum computing deals with systems that contain many quantum bits, providing a new perspective on the physics of systems of many quantum mechanical particles that is complementary to the traditional one. The PI will combine new quantum computing inspired methods with standard condensed matter techniques to gain a better understanding of the landscape of condensed matter phases. One particular benefit of this program is that some of the exotic condensed matter phases studied by the PI may in turn have applications to the design of new quantum computing platforms.Under this award, the PI will support and mentor graduate students throughout their progress to a PhD. The PI will help educate the students in the relevant areas of condensed matter physics, and help them develop proper written and oral communication skills to facilitate the dissemination of their research.TECHNICAL SUMMARY: This award supports theoretical and computational research and education to classify topological quantum phases of matter, including those that are out of equilibrium and those protected by additional symmetries. The PI will combine ideas from condensed matter physics, quantum field theory, and quantum information theory to gain an understanding of these quantum many-body systems. Specifically, the PI will connect the topological features of quantum field theories, such as topological terms in continuum effective actions, to topological invariants that can in principle be directly extracted from a lattice Hamiltonian, such as braiding statistics of anyon or defect excitations. Because a lattice quantum many-body system is essentially a many-qubit system, it is natural that ideas from quantum information theory will naturally be involved in this work. One quantum information idea is that of a non-trivial quantum cellular automaton, which is a generalization of a shallow-depth circuit of local unitaries. The PI will explore the utility of using such quantum cellular automatons to disentangle exotic, “beyond-cohomology,” symmetry protected topological phases of matter.An additional tool that the PI plans to use is that of the conformal bootstrap. This is a numerical technique that constrains the possible conformal field theories that can exist, by putting bounds on their spectra of dimensions of local operators. Building on preliminary work, the PI's team will research how to constrain the conformal field theories that can exist at the boundaries of topological phases, by incorporating the corresponding 't Hooft anomalies into the conformal bootstrap. More generally, the aim of the PI will be to determine how to incorporate information about the non-local operators that appear in topological field-theories into the conformal bootstrap. Furthermore, the PI will also explore topological effects in non-equilibrium settings, such as the recently introduced measurement-induced entanglement transition. Preliminary work by the PI's team has uncovered, for a certain simple instance of this transition, a dual statistical-mechanics model which exhibits a topological phase transition. The PI plans to explore more general versions of this duality.Under this award, the PI will support and mentor graduate students throughout their progress to a PhD. The PI will help educate the students in the relevant areas of condensed matter physics and help them develop proper written and oral communication skills to facilitate the dissemination of their research.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：该奖项支持理论和计算研究和教育，以调查具有许多粒子的量子系统的行为，例如晶体固体中的电子。 大量的电子和它们固有的量子力学性质可以协同作用，导致新的物质状态。 其中包括超导体，它可以零电阻导电，以及量子霍尔态，其中强磁场使电子被限制在二维空间中执行紧密的圆形轨道，从而迫使净电流流向系统的边缘。 PI工作的目标是将理论凝聚态和量子信息理论的联合收割机工具结合起来，以了解量子物质的这些状态。在过去的几年里，量子计算推动了凝聚态理论的重大进展。 量子计算处理包含许多量子比特的系统，为许多量子力学粒子系统的物理学提供了一个新的视角，与传统的观点互补。 PI将联合收割机新的量子计算方法与标准凝聚态技术相结合，以更好地了解凝聚态相的景观。 该项目的一个特别好处是，PI研究的一些奇异凝聚态相可能反过来应用于新量子计算平台的设计。根据该奖项，PI将在研究生攻读博士学位的整个过程中提供支持和指导。 PI将帮助学生在凝聚态物理学的相关领域进行教育，并帮助他们发展适当的书面和口头交流技能，以促进他们的研究的传播。技术概要：该奖项支持理论和计算研究和教育，以分类物质的拓扑量子相，包括那些不平衡的和那些受额外对称性保护的。 PI将结合联合收割机的想法，从凝聚态物理学，量子场论，量子信息理论，以获得这些量子多体系统的理解。 具体来说，PI将把量子场论的拓扑特征（如连续有效作用量中的拓扑项）与原则上可以直接从晶格哈密顿量中提取的拓扑不变量（如任意子或缺陷激发的编织统计）联系起来。 由于晶格量子多体系统本质上是一个多量子比特系统，因此量子信息理论的思想自然会参与这项工作。 一个量子信息的想法是一个非平凡的量子元胞自动机，这是一个局部幺正的浅深度电路的推广。 PI将探索使用这种量子元胞自动机来解开奇异的、“超越上同调”的、对称性保护的物质拓扑相的效用。PI计划使用的另一个工具是共形引导。 这是一种数值技术，通过对局部算子的维数谱进行限制，来约束可能存在的共形场论。 在初步工作的基础上，PI的团队将研究如何通过将相应的't Hooft异常纳入共形引导来约束可以存在于拓扑相边界处的共形场论。 更一般地说，PI的目的将是确定如何将拓扑场论中出现的非局部算子的信息纳入共形引导。 此外，PI还将探索非平衡设置中的拓扑效应，例如最近引入的测量引起的纠缠跃迁。 PI团队的初步工作已经发现，对于这种转变的某个简单实例，一个双重的物理力学模型表现出拓扑相变。 PI计划探索这种二元性的更一般版本。根据该奖项，PI将在研究生攻读博士学位的整个过程中提供支持和指导。 PI将帮助教育学生在凝聚态物理学的相关领域，并帮助他们发展适当的书面和口头沟通技巧，以促进他们的研究传播。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。