论文标题
希尔伯特空间破碎和量子模型中的动态冻结
Hilbert space shattering and dynamical freezing in the quantum Ising model
论文作者
论文摘要
我们在两个空间维度中讨论了横向场ISING模型中的量子动力学。我们表明，直到我们进行量化的高端时间尺度，希尔伯特空间“破碎”到动态断开连接的子行动中。我们将这种破碎识别为源自$ \ mathrm {u}（1）$保护定律的相互作用和单一形式的$ \ mathbb {z} _2 $约束。我们表明，动态断开的扇区的数量在系统体积中是指数级的，并且在系统体积中包括一个子空间指数，即使在没有淬火障碍的情况下，动力学也是完全定位的。根据我们工作的新兴部门的不同，破碎的可能是弱（因此，相对于其新兴的对称部门热典型的初始条件会热能地造成影响（因此，典型的初始条件表现出局部动力学）。我们提供了分析和数值证据，表明弱和强碎片之间的一级样式“冻结过渡”是在非标准的热力学极限下随着对称部门的函数而发生的。我们进一步表明，在过渡域壁动力学的“弱”（熔化）侧遵循普通扩散。
We discuss quantum dynamics in the transverse field Ising model in two spatial dimensions. We show that, up to a prethermal timescale, which we quantify, the Hilbert space 'shatters' into dynamically disconnected subsectors. We identify this shattering as originating from the interplay of a $\mathrm{U}(1)$ conservation law and a one-form $\mathbb{Z}_2$ constraint. We show that the number of dynamically disconnected sectors is exponential in system volume, and includes a subspace exponential in system volume within which the dynamics is exactly localized, even in the absence of quenched disorder. Depending on the emergent sector in which we work, the shattering can be weak (such that typical initial conditions thermalize with respect to their emergent symmetry sector), or strong (such that typical initial conditions exhibit localized dynamics). We present analytical and numerical evidence that a first order-like 'freezing transition' between weak and strong shattering occurs as a function of the symmetry sector, in a non-standard thermodynamic limit. We further numerically show that on the 'weak' (melted) side of the transition domain wall dynamics follows ordinary diffusion.
