Łydżba Patrycja, Prelovšek Peter, Mierzejewski Marcin
Institute of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland.
Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia.
Phys Rev Lett. 2024 May 31;132(22):220405. doi: 10.1103/PhysRevLett.132.220405.
Hilbert space fragmentation is an ergodicity-breaking phenomenon, in which the Hamiltonian shatters into exponentially many dynamically disconnected sectors. In many fragmented systems, these sectors can be labeled by statistically localized integrals of motion, which are nonlocal operators. We study the paradigmatic nearest-neighbor pair hopping model exhibiting the so-called strong fragmentation. We show that this model hosts local integrals of motion (LIOMs), which correspond to frozen density modes with long wavelengths. The latter modes become subdiffusive when longer-range pair hoppings are allowed. Finally, we make a connection with a tilted (Stark) chain. Contrary to the dipole-conserving effective models, the tilted chain is shown to support either a Hamiltonian or dipole moment as an LIOM. Numerical results are obtained from a numerical algorithm, in which finding LIOMs is reduced to a data compression problem.
希尔伯特空间碎片化是一种破遍历性现象，其中哈密顿量分裂成指数级数量的动态不相连扇区。在许多碎片化系统中，这些扇区可以由运动的统计局域积分标记，这些积分是非局域算符。我们研究了表现出所谓强碎片化的典型最近邻对跳跃模型。我们表明，该模型存在局域运动积分（LIOMs），它们对应于长波长的冻结密度模式。当允许更长程的对跳跃时，后一种模式会变成亚扩散模式。最后，我们将其与倾斜（斯塔克）链建立联系。与偶极守恒有效模型相反，倾斜链被证明支持哈密顿量或偶极矩作为LIOM。数值结果是通过一种数值算法获得的，在该算法中，寻找LIOMs被简化为一个数据压缩问题。
