Robustness and Universality of Quantum Many-Body Scars

强相互作用和挫折可以导致量子物质的约束激发。例子包括自旋冰化合物、受抑量子磁体和分数量子霍尔液体。这种受约束的量子物质通常以不再具有简单乘积空间结构的希尔伯特空间为特征。最近，一个约束量子多体系统也已经实现了实验与一维超冷里德伯原子在封锁制度，它可以映射到一个约束硬核玻色子模型。当在远离平衡态的状态下初始化这个系统时，随后的量子动力学被发现具有长寿命的相干振荡动力学;这一观察结果与高度激发态的量子热化动力学的一般预期不一致。一组特殊的本征态，这是几乎从其余的频谱去耦已负责这些长寿的相干动力学。因此，这些状态被称为量子多体伤疤。到目前为止，很大程度上还不清楚这些特殊的本征态有多强大和普遍。本项目的目标是研究一组具有投影约束的多体模型，在多体谱中寻找决定量子动力学的特殊本征态。特别是，我们将集中在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）量子多体眼镜，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，它精确地考虑了问题的约束和对称性，并通过发展基于矩阵乘积态含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疤的普遍性和鲁棒性的理解。除了概念上的重要性，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，因为工程强相互作用和几何挫折可能实现可控的约束量子物质。

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.