Lattice gauge theories, discretized cousins of continuum gauge theories arising in the Standard Model, have become important platforms for exploring non-equilibrium quantum phenomena. Recent works have reported the possibility of disorder-free localization in the lattice Schwinger model. Using degenerate perturbation theory and numerical simulations based on exact diagonalization and matrix product states, we perform a detailed characterization of thermalization breakdown in the Schwinger model, including its spectral properties, structure of eigenstates, and out-of-equilibrium quench dynamics. We scrutinize the strong-coupling limit of the model, in which an intriguing double-logarithmic-in-time growth of entanglement was previously proposed from the initial vacuum state. We identify the origin of this ultraslow growth of entanglement as due to approximate Hilbert space fragmentation and the emergence of a dynamical constraint on particle hopping, which gives rise to sharp jumps in the entanglement entropy dynamics within individual background charge sectors. Based on the statistics of jump times, we argue that entanglement growth, averaged over charge sectors, is more naturally explained as either single-logarithmic or a weak power law in time. Our results suggest the existence of a single ergodicity-breaking regime due to Hilbert space fragmentation, whose properties are reminiscent of conventional many-body localization within numerically accessible system sizes.
Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova（意大利国家核物理研究所（INFN）帕多瓦分部）；Dipartimento di Fisica e Astronomia ”G. Galilei”, Università di Padova（帕多瓦大学伽利略物理与天文学系）；Padua Quantum Technologies Research Center, Università degli Studi di Padova（帕多瓦大学帕多瓦量子技术中心）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig Ma（路德维希...大学物理系及阿诺德·索末菲理论物理中心）
Discrete time crystals enabled by Floquet strong Hilbert space fragmentation
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Department of Physics, City University of Hong Kong（香港城市大学物理系）；South China Normal University（华南师范大学）
Emerging dynamical constraints resulting from inter-site interactions severely limit particle mobility in polar lattice gases. Whereas in absence of disorder hard-core Hubbard models with only strong nearest-neighbor interactions present Hilbert space fragmentation but no many-body localization for typical states, the $1/r^3$ tail of the dipolar interaction results in Hilbert space shattering, as well as in a dramatically slowed down dynamics and eventual disorder-free localization. Our results show that the study of the intriguing interplay between disorder- and interaction-induced many-body …
Investigating many-body localization (MBL) using exact numerical methods is limited by the exponentialgrowth of the Hilbert space. However, localized eigenstates display multifractality and only extend over a vanishing fraction of the Hilbert space. Here, building on this remarkable property, we develop a simple yet efficient decimation scheme to discard the irrelevant parts of the Hilbert space of the random-field Heisenberg chain. This leads to an Hilbert space fragmentation in small clusters, allowing to access larger systems at strong disorder. The MBL transition is quantitatively predicte…
Anderson localization is derived directly from the path integral representation of quantum mechanics in the presence of a random potential energy function. The probability distribution of the potential energy is taken to be a Gaussian in function space with a given autocorrelation function. Averaging the path integral itself we find that the localization length, in one-dimension, is given by (E_{ξ}/σ)(KE_{cl}/σ)ξ where E_{ξ} is the "correlation energy", KE_{cl} the average classical kinetic energy, σ the root-mean-square variation of the potential energy and ξ the autocorrelation length. Avera…
Statistical localization: from strong fragmentation to strong edge modes
由于希尔伯特空间的\emph{strong fragmentation}被分割成不连通的扇区，某些无无序哈密顿算子可以是非遍历的。在这里，我们通过引入“统计局部化运动积分”（SLIOM）的概念来描述这样的系统，其特征值标记了希尔伯特空间的连通分量。SLIOMs在算子意义上不是空间局部化的，但当它们的期望值取在具有有限粒子密度的典型状态时，出现局部化到次广泛区域。我们说明了这一一般概念上的几个哈密顿量，无论是与偶极守恒。此外，我们证明，存在扰动，破坏这些积分的运动在大部分的系统，而保持他们的边界上。这导致在统计上本地化的\emph{strong zero modes}，导致无限长寿命的边缘磁化随着热化块，构成了第一个例子，这样的强边缘模式在不可积模型。我们还表明，在一个特定的例子中，这些边缘模式导致拓扑弦秩序的外观在一定的子集的高度激发本征态。我们提出的一些模型可以在Rydberg量子模拟器中实现。
Role of flavor degrees of freedom in quantum simulations of disorder-free localization
Ludwig Maximilian University of Munich（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics (ASC)（阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of Leeds（利兹大学）；University of Nottingham（诺丁汉大学）；Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems（量子非平衡系统数学与理论物理中心）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Kyung Hee University（庆熙大学）
Exploring Hilbert-Space Fragmentation on a Superconducting Processor
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg（奥格斯堡大学物理所电子关联与磁学理论物理III）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Hefei National Laboratory（合肥国家实验室）
Krylov space perturbation theory for quantum synchronization in closed systems
Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Université Paris-Saclay, CNRS, LPTMS（巴黎萨克雷大学法国国家科学研究中心理论物理与数学实验室）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）
Fate of emergent Hilbert space fragmentation and information insulation upon softening of hard dual constraints at PXP-chain junctions
Department of Physics, School of Mathematical Sciences Ramakrishna Mission Vivekananda Educational and Research Institute（拉马克里希纳使命维韦卡南达教育与研究机构数学科学学院物理系）
Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to conservation laws provide obstructions to thermalization in the absence of disorder. In certain models with dipole and $U(1)$ conservation, the fragmentation results in subdiffusive transport. In this paper we study the interplay between scarring and weak fragmentation giving rise to anomalous hydrodynamics in a class of one-dimensional spin-$1$ frustration-free projector Hamiltonians, known as deformed Motzkin chain. The ground states and low-lying excitations of these chains exhibit large entanglement…
Stark many-body localized (SMBL) systems have been shown both numerically and experimentally to have Bloch many-body oscillations, quantum many-body scars, and fragmentation in the large field tilt limit. Likewise, they are believed to show localization similar to disordered MBL. We explain and analytically prove all these observations by rigorously showing the existence of novel algebraic structures that are exponentially stable in time, which we call dynamical l-bits. Moreover, we show that many-body Bloch oscillations persist even at infinite temperature for exponentially long-times. We num…
Truncation uncertainties for accurate quantum simulations of lattice gauge theories
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Leinweber Institute for Theoretical Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校雷恩韦伯理论物理研究所与物理系）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig Maximilian University of Munich（慕尼黑路德维希-马克西米利安大学物理系与阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Confinement of excitations induces quasilocalized dynamics in disorder-free isolated quantum many-body systems in one spatial dimension. This occurrence is signalled by severe suppression of quantum correlation spreading and of entanglement growth, long-time persistence of spatial inhomogeneities, and long-lived coherent oscillations of local observables. In this work, we present a unified understanding of these dramatic effects. The slow dynamical behavior is shown to be related to the Schwinger effect in quantum electrodynamics. We demonstrate that it is quantitatively captured for long time…
