Yang Zhi-Cheng, Liu Fangli, Gorshkov Alexey V, Iadecola Thomas
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2020 May 22;124(20):207602. doi: 10.1103/PhysRevLett.124.207602.
We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of Z_{2} gauge theory coupled to fermionic matter, leading to a hierarchy of timescales for motion of the fermions. This model can be realized experimentally in two complementary settings.
我们研究一维自旋-1/2模型，其中伊辛畴壁的严格限制导致希尔伯特空间分裂为指数级数量的不相连子空间。尽管之前的大多数工作强调偶极矩守恒是这种分裂的一个基本要素，但我们反而要求与总畴壁数和总磁化强度相关的两个对易的U(1)守恒量。后者自然地源于畴壁的限制。值得注意的是，虽然希尔伯特空间的一些连通分量会热化，但其他分量可通过贝塞耳假设进行求解。我们进一步证明了这种希尔伯特空间分裂模式是如何在与费米子物质耦合的Z₂规范理论的限制极限中微扰地出现的，从而导致费米子运动的时间尺度层次结构。该模型可以在两种互补的实验设置中实现。
