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.

强相互作用和挫折可以导致量子物质的受限激发。例子包括自旋冰化合物、受挫量子磁体和分数量子霍尔液体。这种受限的量子物质通常以希尔伯特空间为特征，而希尔伯特空间不再具有简单的积空间结构。最近，用一维超冷里德伯原子在受限状态下实验实现了一个受限量子多体系统，该系统可以映射到受限硬核玻色子模型上。当在远离平衡状态初始化该系统时，发现随后的量子动力学具有长寿命的相干振荡动力学；这一观察结果与人们对高激发态的量子热化动力学的普遍期望不一致。一组特殊的特征态，几乎与频谱的其余部分解耦，已经被认为是这些长寿命的相干动力学的原因。因此，这些状态被称为量子多体伤痕。到目前为止，还不清楚这些异常特征态有多强健和普遍。本项目的目标是研究一组具有射影约束的多体模型，以寻找决定量子动力学的多体谱中的异常特征态。特别是，我们将重点关注三种不同类型的模型：(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，具有体积排除约束；(3)和投影自旋模型，如AKLT模型。通过发展基于Krylov空间的精确对角化技术，精确地考虑了问题的约束和对称性，以及基于矩阵积态时变分原理的量子动力学的有效描述，我们将获得对约束量子物质中量子多体伤痕的普适性和鲁棒性的理解。除了它们的概念意义之外，理解这些问题对于解释和设计合成量子物质的实验也很重要，因为设计强相互作用和几何挫折可能会实现可控的受限量子物质。