Robustness and Universality of Quantum Many-Body Scars

量子多体疤痕的鲁棒性和普遍性

• 批准号: 425961213
• 负责人: Professor Dr. Michael Knap
• 金额: --
• 依托单位: Arbeitsgruppe Kollektive Quantendynamik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/425961213?language=en
• 关键词: Robustness; Universality; Quantum; Many; Body

Strong interactions and frustration can lead to constrained excitations of quantum matter. Examples include spin-ice compounds, frustrated quantum magnets, and fractional quantum Hall liquids. Such constrained quantum matter are often characterized by a Hilbert space that does not have a simple product space structure anymore. Recently a constrained quantum many-body system has also been realized experimentally with one-dimensional ultracold Rydberg atoms in the blockaded regime, which can be mapped onto a constrained hard core boson model. When initializing this system in a far-from equilibrium state, the ensuing quantum dynamics has been found to feature long-lived coherent oscillatory dynamics; an observation that is at odds with the general expectations for the quantum thermalization dynamics of highly excited states. An exceptional set of eigenstates, which are almost decoupled from the rest of the spectrum have been made responsible for these long-lived coherent dynamics. Therefore, these states were called quantum many-body scars. Thus far, it is largely unclear how robust and universal these exceptional eigenstates are. It is the goal of this project to investigate a set of many-body models, which possess projective constraints, to search for exceptional eigenstates in the many-body spectrum which dictate the quantum dynamics. In particular, we will focus on three different types of models: (1) Gauge theories, whose gauge degree of freedom can be converted to a constraint via Gauss’ law, (2) quantum many-body glasses, which possess volume excluding constraints, (3) and projective spin models, such as the AKLT model. By developing Krylov space based exact diagonalization techniques, which take into account the constraints and the symmetries of the problem exactly, and by developing effective descriptions for the quantum dynamics based on the time-dependent variational principle for matrix product states, we will obtain an understanding for the universality and robustness of quantum many-body scars in constrained quantum matter. Beyond their conceptual significance, understanding these questions will be important for interpreting and devising experiments with synthetic quantum matter, for which engineered strong interactions and geometrical frustration may realize controllable constrained quantum matter.

强相互作用和挫败可能导致量子物质的受约束激发，例如自旋冰化合物、受挫量子磁体和分数量子霍尔液体。此类受约束量子物质通常以不具有简单乘积空间结构的希尔伯特空间为特征。最近，在封锁状态下用一维超冷里德伯原子实验性地实现了约束量子多体系统，在初始化该系统时可以将其映射到约束硬核玻色子模型上。在远离平衡态的情况下，随后的量子动力学被发现具有长寿命的相干振荡动力学；这一观察与对高激发态的量子热化动力学的一般预期不一致，这是一组特殊的本征态。几乎与光谱的其余部分脱钩，导致了这些长期存在的相干动力学，因此，这些状态被称为量子多体疤痕，到目前为止，人们还不清楚这些特殊的本征态有多鲁棒和普遍。该项目的目标是研究一组具有射影约束的多体模型，以寻找多体谱中决定量子动力学的特殊本征态。模型类型：（1）规范理论，其规范自由度可以通过高斯定律转换为约束，（2）量子多体玻璃，其具有排除约束的体积，（3）和射影自旋模型，例如作为 AKLT 模型。开发基于克雷洛夫空间的精确对角化技术，该技术准确地考虑了问题的约束和对称性，并通过基于矩阵乘积状态的时间依赖变分原理的量子动力学的有效描述，我们将加深对受限量子物质中量子多体疤痕的普遍性和鲁棒性除了概念意义外，理解这些问题对于解释和设计合成量子物质实验也很重要，为此，设计强相互作用和几何挫败可能会实现可控。受约束的量子物质。