Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models

Abstract

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...

Slow thermalization of exact quantum many-body scar states under perturbations

“…References [22,23] developed a systematic construction to embed nonthermal states in the spectrum. Many other systems or models have also been discovered or constructed to have scars or scarlike physics [24][25][26][27][28][29][30][31][32][33][34][35].…”

Connection between quantum-many-body scars and the Affleck–Kennedy–Lieb–Tasaki model from the viewpoint of embedded Hamiltonians

“…In other words, two Hamiltonians h 1 b.b+1 and h 2 b,b+1 keep the subspace of the Hilbert space associated with P P XP b,b+1 = 1 and that with P P XP b,b+1 = 0 invariant, and thus we can treat the action of these Hamiltonians in each subspace separately. The commutation relations (24) and (25) can be confirmed directly as…”

“…Analogous to the semiclassical chaotic billiard systems [18], this nonthermalizing behavior is called quantum many-body scars [17,19]. To derive the scars in the PXP model, various theoretical investigations have been attempted including a perturbative approach [20,21], matrix-product state (MPS) representations [19], Floquet random unitary circuits [22], quantum topological phases [23], extending the local Hilbert space for oscillation [24], and the quasiparticle picture [25]. See also a review paper [26].…”

Slow Quantum Thermalization and Many-Body Revivals from Mixed Phase Space

“…Atypical eigenstates had previously been constructed analytically in the AKLT spin chain [15,16], and it has been suggested that some of these non-thermalizing states may be closely related to the ones in the Rydberg atom chain [17,18]. Additionally, various types of non-thermalizing behaviors have since been reported in a number of other models [17,[19][20][21][22][23][24][25][26].…”