Robustness and Universality of Quantum Many-Body Scars

强烈的相互作用和挫折感会导致量子物质的受限激发。例子包括自旋-冰化合物、受挫量子磁铁和分数量子霍尔液体。这种受约束的量子物质通常被描述为一个不再具有简单乘积空间结构的希尔伯特空间。最近，一维超冷里德堡原子也在实验上实现了受约束的量子多体系统，该系统可以映射到受约束的硬核玻色子模型上。当这个系统处于远离平衡态的初始状态时，随后的量子动力学被发现具有长寿命的相干振荡动力学；这一观察结果与人们对高激发态量子热化动力学的普遍预期不符。一组特殊的本征态，几乎与光谱的其余部分解耦，导致了这些长寿命的相干动力学。因此，这些态被称为量子多体疤痕。到目前为止，很大程度上还不清楚这些特殊本征态的健壮性和普适性。这个项目的目标是研究一组具有射影约束的多体模型，在多体光谱中寻找决定量子动力学的例外本征态。特别是，我们将重点介绍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，其体积不包括约束；(3)以及投射自旋模型，如AKLT模型。通过发展基于Krylov空间的精确对角化技术，精确地考虑问题的约束和对称性，通过发展基于矩阵乘积态含时变分原理的量子动力学有效描述，我们将获得对约束量子物质中量子多体疤痕的普适性和健壮性的理解。除了概念上的意义，理解这些问题对于解释和设计合成量子物质的实验将是重要的，对合成量子物质来说，工程设计的强相互作用和几何受挫可能实现可控的受限量子物质。

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.