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.

非技术摘要：该奖项支持理论和计算研究和教育，以研究具有许多粒子的量子系统的行为，例如晶体固体中的电子。大量的电子及其继承的量子机械性质可以一致发挥作用，导致物质的新状态。其中包括可以用零电阻进行电力的超导体和量子霍尔状态，其中强磁场会导致局限于两个维度的电子执行紧密的圆形轨道，从而迫使净电流流向系统的边缘。 PI工作的目的是结合理论凝结物质和量子信息理论的工具，以了解对这些量子物质状态的理解。在过去的几年中，量子计算在凝结物质理论中融合了重大进展。量子计算涉及包含许多量子位的系统，为许多量子机械颗粒的系统物理学提供了新的视角，这些量子是与传统粒子互补的。 PI将将新的量子计算方法与标准的冷凝物质技术相结合，以更好地了解冷凝物质阶段的景观。该计划的一个特别好处是，PI可能会在设计新的量子计算平台的设计中申请了一些异国情调的凝结物阶段。在此奖项之后，PI将在整个奖项中支持和精神生学生在博士学位的过程中提供支持和精神学生。 PI将帮助教育学生在相关的物理物理学的相关领域，并帮助他们发展适当的书面和口头沟通能力，以促进他们的研究传播。技术摘要：该奖项支持理论和计算研究和教育，以对物质的拓扑量子阶段进行分类，包括在其他符号和其他对符号的范围内的拓扑量子阶段。 PI将结合凝结物理学，量子场理论和量子信息理论中的思想，以了解这些量子多体系统。具体而言，PI将将量子场理论的拓扑特征（例如连续有效动作中的拓扑术语）连接到可以直接从晶格汉密尔顿（Hamiltonian）中直接提取的拓扑不变性，例如任何或缺陷兴奋的编织统计数据。由于晶格量子多体系统本质上是一个多数的系统，因此自然而然地，量子信息理论的想法自然会参与这项工作。一种量子信息的想法是非平凡的量子细胞自动机，这是对局部单元浅深度电路的概括。 PI将探索使用此类量子细胞自动机以将物质的对称性拓扑阶段进行解散的“超级人体学”。这是一种数值技术，它通过将界限放在本地运算符的尺寸上来限制可能存在的共形场理论。在初步工作的基础上，PI的团队将研究如何通过将相应的Hooft异常将相应的Hooft异常纳入共形引导程序中来限制在拓扑阶段边界上可能存在的保形场理论。更笼统地，PI的目的是确定如何将出现在拓扑田间理论中的非本地运算符的信息中纳入整形自举。此外，PI还将探索非平衡环境中的拓扑作用，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揭示了这种过渡的某个简单实例，这是一种表现出拓扑相变的双重统计力学模型。 PI计划探索这种二元性的更一般版本。在此奖项下，PI将在整个博士学位的过程中支持和精神生学生。 PI将帮助教育学生在凝聚态物理学的相关领域中教育学生，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的法定任务，并被认为是通过基金会的知识分子优点和更广泛的审查标准通过评估来评估的。