Constraint-induced breaking and restoration of ergodicity in spin-1 PXP models,Physical Review Research

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Constraint-induced breaking and restoration of ergodicity in spin-1 PXP models
Physical Review Research ( IF 3.5 ) Pub Date : 2021-08-31 , DOI: 10.1103/physrevresearch.3.033201
Bhaskar Mukherjee _{1,

2} , Zi Cai _{1,

3,

4} , W. Vincent Liu _{1,

2,

4,

5,

6}

Affiliation

Eigenstate thermalization hypothesis (ETH) has played a pivotal role in understanding ergodicity and its breaking in isolated quantum many-body systems. The recent experiment on 51-atom Rydberg quantum simulator by Bernien et al. [Nature (London) 551, 579 (2017)] and subsequent theoretical analysis have shown that hardcore kinetic constraint can lead to weak ergodicity breaking. In this work, we demonstrate, using

1 d

spin-1 PXP models, that miscellaneous type of ergodicity can be realized by adjusting the hardcore constraints between different components of nearest-neighbor spins. This includes ETH violation due to emergent shattering of Hilbert space into exponentially many subsectors of various sizes, a novel form of nonintegrability with an extensive number of local conserved quantities and strong ergodicity. We analyze these different forms of ergodicity and study their impact on the nonequilibrium dynamics of a

Z_{2}

initial state. We use forward-scattering approximation to understand the amount of

Z_{2}

oscillation present in these models. Our work shows that not only ergodicity breaking but an appropriate choice of constraints can lead to restoration of ergodicity as well.

中文翻译：

在自旋 1 PXP 模型中约束引起的破坏和遍历性的恢复

本征态热化假说 (ETH) 在理解遍历性及其在孤立量子多体系统中的破坏方面发挥了关键作用。Bernien等人最近对 51 原子里德堡量子模拟器进行的实验。[ Nature (London) 551 , 579 (2017)] 和随后的理论分析表明，硬核动力学约束会导致弱遍历性破坏。在这项工作中，我们演示，使用

1 d

spin-1 PXP 模型，可以通过调整最近邻自旋的不同分量之间的硬核约束来实现杂项类型的遍历性。这包括由于 Hilbert 空间突然破碎成指数级许多不同大小的子扇区而导致的 ETH 违规，这是一种具有大量局部守恒量和强遍历性的新形式的不可积性。我们分析了这些不同形式的遍历性，并研究了它们对非平衡动力学的影响。