In this work, based on the Fredkin spin chain, we introduce a family of spin-$1/2$ many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved spin configuration in the 1D Fermi-Hubbard model in the infinite onsite repulsion limit. To demonstrate the many-body scars, we construct an exact eigenstate that is in the middle of the spectrum within each fractured sub-sector displaying either logarithmic or area-law entanglement entropy. The interplay between fragmentation and scarring leads to rich tunable non-ergodic dynamics by quenching different initial states that is shown through large scale matrix product state simulations. In addition, we provide a Floquet quantum circuit that displays non-ergodic dynamics as a result of sharing the same fragmentation structure and scarring as the Hamiltonian.
The discovery of Quantum Many-Body Scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki (AKLT) spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of syste…
Motivated by recent observations of ergodicity breaking due to Hilbert space fragmentation in 1D Fermi-Hubbard chains with a tilted potential [Scherg et al., arXiv:2010.12965], we show that the same system also hosts quantum many-body scars in a regime $U\approx Δ\gg J$ at electronic filling factor $ν=1$. We numerically demonstrate that the scarring phenomenology in this model is similar to other known realisations such as Rydberg atom chains, including persistent dynamical revivals and ergodicity-breaking many-body eigenstates. At the same time, we show that the mechanism of scarring in the F…
Aspects of Hilbert space fragmentation in the quantum East model: fragmentation, subspace-restricted quantum scars, and effects of density-density interactions
本文解析刻画量子 East 模型的 Hilbert 空间碎裂与子空间受限量子伤疤，并揭示密度–密度相互作用导致的谱学转变及无限耦合可积极限。
Rydberg atoms in optical tweezer arrays provide a playground for nonequilibrium quantum many-body physics. The PXP model describes the dynamics of such systems in the strongly interacting Rydberg blockade regime and notably exhibits weakly nonergodic dynamics due to quantum many-body scars. Here, we study the PXP model in a strong staggered external field, which has been proposed to manifest quasiparticle confinement in light of a mapping to a lattice gauge theory. We characterize this confining regime using both numerical exact diagonalization and perturbation theory around the strong-field l…
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…
Engineering non-ergodic properties in two dimensional quantum many-body systems
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Materials Science and Engineering, National University of Singapore（新加坡国立大学材料科学与工程系）；INPHYNI, Université Côte d’Azur, CNRS（尼斯蔚蓝海岸大学CNRS INPHYNI研究所）；Department of Physics, Washington University in St. Louis（圣路易斯华盛顿大学物理系）
Recent studies of interacting systems of quantum spins, ultracold atoms and correlated fermions have shed a new light on how isolated many-body systems can avoid rapid equilibration to their thermal state. It has been shown that many such systems can "weakly" break ergodicity: they possess a small number of non-thermalising eigenstates and/or display slow relaxation from certain initial conditions, while majority of other initial states equilibrate fast, like in conventional thermalising systems. In this chapter, we provide a pedagogical introduction to weak ergodicity breaking phenomena, incl…
