Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session W66: Quantum ManyBody ScarsInvited

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Sponsoring Units: DCMP Chair: Nicolas Regnault, Ecole Normale Superieure Room: Four Seasons 1 
Friday, March 6, 2020 8:00AM  8:36AM 
W66.00001: Quantum manybody scars: a new form of weak ergodicity breaking in constrained quantum systems Invited Speaker: Zlatko Papic Recent experiments on large chains of Rydberg atoms [1] have demonstrated the possibility of realising onedimensional, kinetically constrained quantum systems. It was found that such systems exhibit surprising signatures of nonergodic dynamics, such as robust periodic revivals in global quenches from certain initial states. This weak form of ergodicity breaking has been interpreted as a manifestation of "quantum manybody scars" [2], i.e., the manybody analogue of unstable classical periodic orbits of a single particle in a chaotic stadium billiard. Scarred manybody eigenstates have been shown to exhibit a range of unusual properties which violate the Eigenstate Thermalisation Hypothesis, such as equidistant energy separation, anomalous expectation values of local observables and subthermal entanglement entropy. I will demonstrate that these properties can be understood using a tractable model based on a single particle hopping on the Hilbert space graph, which formally captures the idea that scarred eigenstates form a representation of a large SU(2) spin that is embedded in a thermalising manybody system. I will show that this picture allows to construct a more general family of scarred models where the fundamental degree of freedom is a quantum clock [3]. These results suggest that scarred manybody bands give rise to a new universality class of constrained quantum dynamics, which opens up opportunities for creating and manipulating novel states with longlived coherence in systems that are now amenable to experimental study. 
Friday, March 6, 2020 8:36AM  9:12AM 
W66.00002: Quantum manybody scars: connections to integrability and stability Invited Speaker: Anushya Chandran Quantum manybody scar states are exceptional finite energy density eigenstates in an otherwise thermalizing system that do not satisfy the eigenstate thermalization hypothesis. Recent atomic array experiments in the Rydberg blockaded regime suggests that the simplest blockaded Hamiltonian, the PXP Hamiltonian, has such scars in its spectrum. In this talk, I will discuss the connections between integrability and quantum scars by identifying a proximate integrable point at which the nonthermal signatures of the scar states become more pronounced. I will further discuss the stability of quantum scars to generic perturbations. Although the scar states hybridize with the other states in the spectrum upon perturbation, their nonthermal properties survive for a parametrically long time in quench experiments. 
Friday, March 6, 2020 9:12AM  9:48AM 
W66.00003: Weak Ergodicity Breaking and Quantum ManyBody Scars in Spin1 XY Magnets Invited Speaker: Thomas Iadecola We study the spin1 XY model on a hypercubic lattice in d dimensions and show that this wellknown nonintegrable model hosts an extensive set of anomalous finiteenergydensity eigenstates with remarkable properties. Namely, they exhibit subextensive entanglement entropy and spatiotemporal longrange order, both believed to be impossible in typical highly excited eigenstates of nonintegrable quantum manybody systems. While generic initial states are expected to thermalize, we show analytically that the eigenstates we construct lead to weak ergodicity breaking in the form of persistent oscillations of local observables following certain quantum quenches—in other words, these eigenstates provide an archetypal example of socalled quantum manybody scars. This work opens the door to the analytical study of the microscopic origin, dynamical signatures, and stability of such phenomena. 
Friday, March 6, 2020 9:48AM  10:24AM 
W66.00004: Phenomenology and mechanisms of Quantum manybody scarring Invited Speaker: Wen Wei Ho A central postulate of statistical mechanics is ergodicity  a generic interacting, quantum manybody system initialized out of equilibrium is expected to explore its allowed phase phase and eventually thermalize. Known exceptions to this behavior include strongly disordered, manybody localized (MBL) systems, and finelytuned integrable systems. In this talk, I will discuss a different mechanism pertaining to a weak form of ergodicity breaking: Quantum manybody scarring (QMBS) [1]. Motivated by recent quench experiments with Rydberg atom arrays [2] which observed surprisingly slow thermalizing dynamics from certain simple initial states, QMBS is tied to the presence of special, eigenstate thermalization hypothesis(ETH)violating eigenstates in the manybody spectrum. I will first discuss how a variational description of the manybody dynamics seen in the experiments, using the timedependent variational principle (TDVP) over a manifold of entangled matrixproduct states, can capture this nonthermalizing dynamics and furthermore provide some insight into the connection to the similarly named phenomenon of quantum scars in singleparticle chaos in terms of isolated, unstable, periodic orbits [3]. I will also discuss a complementary approach in which the scarred states can be understood as arising from an embedded su(2) symmetric subspace [4]. More generally, I will discuss physical mechanisms giving rise to QMBS in other settings that can be analytically understood, such as from the idea of embedded Hamiltonians [5] and from the dynamics of virtual entangled pairs [6]. 
Friday, March 6, 2020 10:24AM  11:00AM 
W66.00005: Integrability, Thermalization, and Quantum Scars in a Constrained Hamiltonian Invited Speaker: Sanjay Moudgalya We study the quantum dynamics of a simple translation invariant, centerofmass preserving model of interacting fermions in one dimension, which arises in multiple experimentally realizable contexts. We show that this model exhibits a Hilbert space that fractures into exponentially many dynamically disconnected Krylov subspaces. Each of the exponentially large Krylov subspaces can either be integrable or nonintegrable. We analytically find examples of several integrable subspaces, and show evidence for the validity of Eigenstate Thermalization Hypothesis (ETH) restricted to each nonintegrable subspace. This model thus exhibits phenomenology associated with quantum scars, i.e. the fate of an initial product state under timeevolution depends on the properties of the Krylov subspaces it has weights in. In addition, some of the nonintegrable Krylov subspaces show conventional quantum scars, which manifest as revivals and slow thermalization of certain charge density wave configurations. 
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