近日，德国马克斯普朗克量子光学研究所的Johannes Zeiher及其研究团队取得一项新进展。经过不懈努力，他们成功观察到二维希尔伯特空间破碎和分形激励。相关研究成果已于2024年11月13日在国际权威学术期刊《自然》上发表。

据悉，非平衡态孤立量子系统的弛豫行为，是多体物理学中最引人入胜的问题之一。处于非平衡态的量子系统，通常通过扰乱局部信息和建立纠缠熵来弛豫至热平衡态。然而，哈密顿量中的动力学约束可导致这一基本范式的失效，因为底层希尔伯特空间会碎裂成动态解耦的子区域，在这些子区域内，热化过程可能会受到强烈抑制。

该研究团队在二维倾斜玻色-哈伯德模型中，实验观察到了希尔伯特空间碎裂现象。利用量子气体显微镜技术，研究人员构建了多种初始状态，并发现了希尔伯特空间碎裂的丰富表现，涉及体状态、界面和缺陷，即二维、一维和零维对象。

具体而言，粒子数和能量均等的均匀初始状态在弛豫动力学上表现出显著差异。在全局非热化的棋盘状态上引入受控缺陷后，研究人员观察到了高度各向异性的次维动力学，这是其分形性质的直接体现。而局域态与热化态之间的界面则表现出依赖于其方向的动力学特征。

这项研究结果不仅标志着在超越一维的体系中，观察到了希尔伯特空间破碎现象，还同时直接观察到了分形子，为深入研究受限系统中的微观传输现象奠定了基础。

附：英文原文

Title: Observation of Hilbert space fragmentation and fractonic excitations in 2D

Author: Adler, Daniel, Wei, David, Will, Melissa, Srakaew, Kritsana, Agrawal, Suchita, Weckesser, Pascal, Moessner, Roderich, Pollmann, Frank, Bloch, Immanuel, Zeiher, Johannes

Issue&Volume: 2024-11-13

Abstract: The relaxation behaviour of isolated quantum systems taken out of equilibrium is among the most intriguing questions in many-body physics. Quantum systems out of equilibrium typically relax to thermal equilibrium states by scrambling local information and building up entanglement entropy. However, kinetic constraints in the Hamiltonian can lead to a breakdown of this fundamental paradigm owing to a fragmentation of the underlying Hilbert space into dynamically decoupled subsectors in which thermalization can be strongly suppressed. Here we experimentally observe Hilbert space fragmentation in a two-dimensional tilted Bose–Hubbard model. Using quantum gas microscopy, we engineer a wide variety of initial states and find a rich set of manifestations of Hilbert space fragmentation involving bulk states, interfaces and defects, that is, two-, one- and zero-dimensional objects. Specifically, uniform initial states with equal particle number and energy differ strikingly in their relaxation dynamics. Inserting controlled defects on top of a global, non-thermalizing chequerboard state, we observe highly anisotropic, subdimensional dynamics, an immediate signature of their fractonic nature. An interface between localized and thermalizing states in turn shows dynamics depending on its orientation. Our results mark the observation of Hilbert space fragmentation beyond one dimension, as well as the concomitant direct observation of fractons, and pave the way for in-depth studies of microscopic transport phenomena in constrained systems.

DOI: 10.1038/s41586-024-08188-0

Source: https://www.nature.com/articles/s41586-024-08188-0