Session W66: Quantum Many-Body Scars

Quantum many-body scars: a new form of weak ergodicity breaking in constrained quantum systems

Recent experiments on large chains of Rydberg atoms [1] have demonstrated the possibility of realising one-dimensional, kinetically constrained quantum systems. It was found that such systems exhibit surprising signatures of non-ergodic 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 many-body scars" [2], i.e., the many-body analogue of unstable classical periodic orbits of a single particle in a chaotic stadium billiard. Scarred many-body 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 many-body 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 many-body bands give rise to a new universality class of constrained quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.

[1] H. Bernien et al., Nature 551, 579 (2017).
[2] C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, Z. Papic, Nat. Phys. 14, 745 (2018).
[3] Kieran Bull, Ivar Martin, and Z. Papic, Phys. Rev. Lett. 123, 030601 (2019).   

Quantum many-body scars: connections to integrability and stability

Quantum many-body 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 non-thermal 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.   

Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets

We study the spin-1 XY model on a hypercubic lattice in d dimensions and show that this well-known nonintegrable model hosts an extensive set of anomalous finite-energy-density eigenstates with remarkable properties. Namely, they exhibit subextensive entanglement entropy and spatiotemporal long-range order, both believed to be impossible in typical highly excited eigenstates of nonintegrable quantum many-body 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 so-called quantum many-body scars. This work opens the door to the analytical study of the microscopic origin, dynamical signatures, and stability of such phenomena.   

Phenomenology and mechanisms of Quantum many-body scarring

A central postulate of statistical mechanics is ergodicity -- a generic interacting, quantum many-body system initialized out of equilibrium is expected to explore its allowed phase phase and eventually thermalize. Known exceptions to this behavior include strongly disordered, many-body localized (MBL) systems, and finely-tuned integrable systems. In this talk, I will discuss a different mechanism pertaining to a weak form of ergodicity breaking: Quantum many-body 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 many-body spectrum. I will first discuss how a variational description of the many-body dynamics seen in the experiments, using the time-dependent variational principle (TDVP) over a manifold of entangled matrix-product states, can capture this non-thermalizing dynamics and furthermore provide some insight into the connection to the similarly named phenomenon of quantum scars in single-particle 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].

[1] Nat. Phys. 14, 745–749 (2018)
[2] Nature 551, 579–584 (2017)
[3] Phys. Rev. Lett. 122, 040603 (2019)
[4] Phys. Rev. Lett. 122, 220603 (2019)
[5] Phys. Rev. Lett. 119, 030601 (2019)
[6] arXiv:1910.08101   

Integrability, Thermalization, and Quantum Scars in a Constrained Hamiltonian

We study the quantum dynamics of a simple translation invariant, center-of-mass 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 non-integrable. We analytically find examples of several integrable subspaces, and show evidence for the validity of Eigenstate Thermalization Hypothesis (ETH) restricted to each non-integrable subspace. This model thus exhibits phenomenology associated with quantum scars, i.e. the fate of an initial product state under time-evolution depends on the properties of the Krylov subspaces it has weights in. In addition, some of the non-integrable Krylov subspaces show conventional quantum scars, which manifest as revivals and slow thermalization of certain charge density wave configurations.