一类疤痕无挫挫哈密顿量中的反常流体动力学
Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
摘要：
非典型本征态的形式量子疤痕和希尔伯特空间的碎片，由于守恒定律提供的障碍，热化在没有无序。在偶极和$U(1)$守恒的某些模型中，碎裂导致亚扩散输运。在本文中，我们研究的疤痕和弱碎裂之间的相互作用，引起异常流体动力学的一类一维自旋$1$挫折免费投影哈密顿，被称为变形Motzkin链。这些链的基态和低激发态表现出大的纠缠和临界减速。我们表明，在高能量的特定形式的投影仪导致出现不相交的Krylov子空间的开放边界条件下，与一个确切的量子疤痕被嵌入在每个子空间，导致纠缠和本地化的动力学增长缓慢的特定出平衡的初始状态。此外，专注于无限的温度，我们揭示了自旋输运是亚扩散，我们证实了约束随机元胞自动机电路的模拟。与偶极矩守恒系统相比，变形Motzkin链似乎属于不同的普适类，具有不同的动力学输运指数和多项式的Krylov子空间。
英文摘要：
Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to conservation laws provide obstructions to thermalization in the absence of disorder. In certain models with dipole and $U(1)$ conservation, the fragmentation results in subdiffusive transport. In this paper we study the interplay between scarring and weak fragmentation giving rise to anomalous hydrodynamics in a class of one-dimensional spin-$1$ frustration-free projector Hamiltonians, known as deformed Motzkin chain. The ground states and low-lying excitations of these chains exhibit large entanglement and critical slowdown. We show that at high energies the particular form of the projectors causes the emergence of disjoint Krylov subspaces for open boundary conditions, with an exact quantum scar being embedded in each subspace, leading to slow growth of entanglement and localized dynamics for specific out-of-equilibrium initial states. Furthermore, focusing on infinite temperature, we unveil that spin transport is subdiffusive, which we corroborate by simulations of constrained stochastic cellular automaton circuits. Compared to dipole moment conserving systems, the deformed Motzkin chain appears to belong to a different universality class with distinct dynamical transport exponent and only polynomially many Krylov subspaces.
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