论文标题
强烈的希尔伯特空间碎片通过在二维中的新兴量子鼓碎片化
Strong Hilbert space fragmentation via emergent quantum drums in two dimensions
论文作者
论文摘要
我们在受约束的希尔伯特空间中引入了$ s = 1/2 $的无疾病模型，在晶格的任何两个相邻地点上，不允许同时使用两个上旋转。相互作用是通过响环术语给出的，对基本斑块进行了保存，既保存总磁化强度和偶极矩。我们表明，该模型提供了一个可进行的典型示例，即在二维中具有典型的初始状态，相对于完整的希尔伯特空间，其典型的初始状态在二维中提供了一个可行的例子。鉴于任何产品状态，该系统可以分解为由边缘和/或顶点共享的不相交的空间区域，我们将我们称为``量子鼓''。这些量子鼓有多种形状和尺寸，并指定属于鼓固定其频谱的plaquettes。分析计算一些小鼓的光谱。我们在数值上研究了两个较大的准二维鼓，分别称为``电线''和``两条线的连接''。我们发现，这些谱系具有混乱的频谱，但也支持不同的量子多体疤痕系列，这些量子会导致不同初始状态的定期复兴。该线被证明等同于具有开放边界的一维PXP链，这是一种用于量子多体疤痕的范式模型。而两根电线的连接代表了一个独特的约束模型。
We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as ``quantum drums''. These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed ``wire'' and a ``junction of two wires'' respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.
