Discrete Time-Crystalline Order Enabled by Quantum Many-Body Scars: Entanglement Steering via Periodic Driving

Abstract

The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.

Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model

“…( 15) is already simple enough to work with and it has been investigated for various models and settings, see e.g. [20][21][22][23][24][25][26][27][28][30][31][32][33]…”

“…In the course of the Floquet protocol, the components of P k and Q k are updated via Eq. (D34), which follows from the relation (28). Then, in order to gain insight on the structure of V k for f T = 2π/9 and JT = 4π/9 (or vice versa), let us plot the components of P k and Q k for different values of k and see how they change across the chain as the number of periods k increases.…”

“…The case of long-range entanglement is traditionally of special interest, since it plays a key role in the understanding of various many-body phenomena, with the paradigmatic example being the quantum magnetism [19]. A powerful tool for generating states with a long-range entanglement and other non-trivial properties is provided by the periodic (Floquet) driving, which allows steering the dynamics to the desired state by a sequence of discrete time steps [20][21][22][23][24][25][26][27][28]. Recently, this method has been used in the realization of exotic nonequilibrium quantum many-body states, such as discrete time crystals [28] and quantum many-body scars [28,29].…”

“…A powerful tool for generating states with a long-range entanglement and other non-trivial properties is provided by the periodic (Floquet) driving, which allows steering the dynamics to the desired state by a sequence of discrete time steps [20][21][22][23][24][25][26][27][28]. Recently, this method has been used in the realization of exotic nonequilibrium quantum many-body states, such as discrete time crystals [28] and quantum many-body scars [28,29]. A periodic driving protocol for on-demand generation of long-range entanglement has been suggested for a system of ultracold atoms in optical superlattices, a setup which simulates the one-dimensional (1D) spin-1/2 Heisenberg model with time-dependent exchange interaction [20].…”

Temporal evolution of one-dimensional fermion liquid with particle loss

“…For critical systems, entanglement entropy has logarithmic scaling behavior [66,70,71]. Under temporal evolution, Von Neumann entropy also tracks the universal dynamical properties of correlations in various systems, including unitary [72][73][74][75][76][77] or non-unitary quantum quench [78,79], and generic dissipative system [80][81][82][83] and generic stochastic [84][85][86][87][88][89][90][91][92] dynamics in isolated, time-periodic driven system [93][94][95][96], or nonequilibrium systems [90,[97][98][99].…”