We introduce a family of non-integrable 1D lattice models that feature robust periodic revivals under a global quench from certain initial product states, thus generalizing the phenomenon of many-body scarring recently observed in Rydberg atom quantum simulators. Our construction is based on a systematic embedding of the single-site unitary dynamics into a kinetically-constrained many-body system. We numerically demonstrate that this construction yields new families of models with robust wave-function revivals, and it includes kinetically-constrained quantum clock models as a special case. We show that scarring dynamics in these models can be decomposed into a period of nearly free clock precession and an interacting bottleneck, shedding light on their anomalously slow thermalization when quenched from special initial states.Introduction.-The understanding of ergodicity and thermalization in isolated quantum systems is an open problem in many-body physics, with important implications for a variety of experimental systems [1][2][3][4][5]. On the one hand, this problem has inspired important developments such as Eigenstate Thermalization Hypothesis (ETH) [6][7][8], which establishes a link between ergodicity and the properties of the system's eigenstates. On the other hand, strong violation of ergodicity can result in rich new physics, such as in integrable systems [9], Anderson insulators [10], and many-body localized phases [11][12][13]. In these cases, the emergence of many conservation laws prevents the system, initialized in a random state, from fully exploring all allowed configurations in the Hilbert space, causing a strong ergodicity breaking.A recent experiment on an interacting quantum simulator [14] has reported a surprising observation of quantum dynamics that is suggestive of weak ergodicity breaking. Utilizing large 1D chains of Rydberg atoms [14-16], the experiment showed that quenching the system from a Néel initial state lead to persistent revivals of local observables, while other initial states exhibited fast equilibration without any revivals. The stark sensitivity of the system's dynamics to the initial states, which were all effectively drawn from an "infinite temperature" ensemble, appeared at odds with "strong" ETH [17][18][19].In Ref. 20 and 21 the non-ergodic dynamics of a Rydberg atom chain was interpreted as a many-body generalization of the classic phenomenon of quantum scar [22]. For a quantum particle in a stadium billiard, scars represent an anomalous concentration of the particle's trajectory around (unstable) periodic orbits in the corresponding classical system, which has an impact on optical and transport properties [23][24][25]. By contrast, in the strongly interacting Rydberg atom chain initialized in the Néel state, quantum dynamics remains concentrated around a small subset of states in the many-body Hilbert space, thus it is effectively "semiclassical" [21]. While recent works [26,27] have shown that revivals can be significantly enhanced by certain perturbations to the syst...

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which both Synthetic Minority Oversampling Technique (SMOTE) and permutations of the CICY matrix are used to decrease the class imbalance and improve performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned. * kieran.bull@seh.ox.ac.uk † hey@maths.ox.ac.uk ‡ vishnu@neo.phys.wits.ac.za

We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple su(2) Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, |Zn , including ones that show no revivals in the unperturbed PXP model. We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models. arXiv:2001.08232v1 [cond-mat.str-el]

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Supervised machine learning can be used to predict properties of string geometries with previously unknown features. Using the complete intersection Calabi-Yau (CICY) threefold dataset as a theoretical laboratory for this investigation, we use low h 1,1 geometries for training and validate on geometries with large h 1,1 . Neural networks and Support Vector Machines successfully predict trends in the number of Kähler parameters of CICY threefolds.The numerical accuracy of machine learning improves upon seeding the training set with a small number of samples at higher h 1,1 . * pykb@leeds.ac.uk † hey@maths.ox.ac.uk ‡ vishnu@neo.phys.wits.ac.za