Interacting dynamics and exotic phases of quantum lattice systems

量子晶格系统的相互作用动力学和奇异相

• 批准号: RGPIN-2018-03733
• 负责人: Bachmann, Sven
• 金额: $ 1.68万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=679294
• 关键词: Interacting; dynamics; exotic; phases; quantum

Quantum lattice systems lie at the intersection of many-body condensed matter physics, quantum information theory and, generally, mathematical statistical physics. The overall objective of this project is to explore the analytic structure of these quantum mechanical models that describe condensed matter at the microscopic scale. Physically motivated questions that arose in the context of the quantum Hall effect, recently driven by quantum information theory and supported by experiments in optical lattices, shall be put in a mathematical framework where spectral, dynamical and statistical mechanical questions can be addressed.******The project aims at developing algebraic and analytic methods to lay the foundations of a rigorous study of novel exotic states of matter characterized by topological order or many-body localization. Handling the specific difficulties arising in particular from the non-perturbative nature of interactions between an arbitrarily large number of particles requires an extension of our knowledge of the statistical mechanics of infinite quantum lattice systems: dynamical locality, properties of ground states, structure of eigenstates, and effects of disorder.******The project is organized in three principal themes. The first builds on very recent results concerning the driven dynamics of quantum lattice systems to obtain a general C*-algebraic adiabatic theory in the infinite volume limit, with improved, exponential error bounds. The second aims at a better understanding of the invariants of topological matter, such as (fractional) quantum Hall systems and topological insulators, in an interacting setting. The third theme is to push the quasi-adiabatic continuation technique beyond the domain of its current and very successful application, in particular to gapless disordered systems. Expected further applications of the program range from spectral stability results to a better understanding of the correlation structure of dynamically localized quantum lattice systems.******HQPs recruited specifically for this project will be involved in all stages, with research questions adapted to their level of technical abilities and to the time horizon set by their program.

量子晶格系统位于多体凝聚态物理学、量子信息论和数学统计物理学的交叉点。该项目的总体目标是探索这些在微观尺度上描述凝聚态物质的量子力学模型的分析结构。最近由量子信息理论驱动并得到光学晶格实验支持的量子霍尔效应背景下出现的物理问题，应置于可以解决光谱、动力学和统计力学问题的数学框架中。******该项目旨在开发代数和分析方法，为严格研究以拓扑序或多体局域化为特征的新颖奇特物质状态奠定基础。处理特别是由于任意大量粒子之间相互作用的非微扰性质而产生的具体困难，需要扩展我们对无限量子晶格系统统计力学的知识：动力学局部性、基态性质、本征态结构和无序效应。******该项目由三个主要主题组成。第一个基于有关量子晶格系统驱动动力学的最新结果，以获得无限体积极限下的通用 C* 代数绝热理论，并具有改进的指数误差界限。第二个目标是更好地理解相互作用环境中拓扑物质的不变量，例如（分数）量子霍尔系统和拓扑绝缘体。第三个主题是将准绝热连续技术推向其当前非常成功的应用领域之外，特别是无间隙无序系统。该计划的进一步应用范围包括从光谱稳定性结果到更好地理解动态定域量子晶格系统的相关结构。******专门为该项目招募的 HQP 将参与所有阶段，研究问题将适应他们的技术能力水平和其计划设定的时间范围。