Fractal nature of high-order time crystal phases

Abstract

Discrete Floquet time crystals (DFTC) are characterized by the spontaneous breaking of the discrete time-translational invariance characteristic of Floquet driven systems. In analogy with equilibrium critical points, also time-crystalline phases display critical behaviour of different order, i.e., oscillations whose period is a multiple $p>2$ of the Floquet driving period. Here, we introduce a new, experimentally-accessible, order parameter which is able to unambiguously detect crystalline phases regardless of the value of $p$ and, at the same time, is a useful tool for chaos diagnostic. This new paradigm allows us to investigate the phase diagram of the long-range (LR) kicked Ising model to an unprecedented depth, unveiling a rich landscape characterized by self-similar fractal boundaries. Our theoretical picture describes the emergence of DFTCs phase both as a function of the strength and period of the Floquet drive, capturing the emergent ${\mathbb{Z}}_p$ symmetry in the Floquet-Bloch waves.

References in corpus (23)

• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum computing with trapped ions
• Cold atoms in cavity-generated dynamical optical potentials
• Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Dynamical obstruction to localization in a disordered spin chain
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• A Guide to Stochastic Loewner Evolution and its Applications
• Markovian baths and quantum avalanches
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• A constructive theory of the numerically accessible many-body localized to thermal crossover
• Is there slow particle transport in the MBL phase?
• Thermalization of dilute impurities in one dimensional spin chains
• Metastability and discrete spectrum of long-range systems
• Discrete time-crystalline response stabilized by domain-wall confinement
• Emergent parametric resonances and time-crystal phases in driven BCS systems
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• Critical properties of the prethermal Floquet Time Crystal
• Stroboscopic aliasing in long-range interacting quantum systems
• Critical properties of the Floquet time crystal within the Gaussian approximation
• Entanglement propagation and dynamics in non-additive quantum systems

Cited by in corpus (15)

• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Floquet time-crystals as sensors of AC fields
• Prethermal Floquet time crystals in chiral multiferroic chains and applications as quantum sensors of AC fields
• Hybrid Stabilizer Matrix Product Operator
• Theory of robust quantum many-body scars in long-range interacting systems
• Entanglement propagation and dynamics in non-additive quantum systems
• Prethermalization in aperiodically driven classical spin systems
• Stabilization of Discrete Time-Crystaline Response on a Superconducting Quantum Computer by increasing the Interaction Range
• Semiclassical Quantum Trajectories in the Monitored Lipkin-Meshkov-Glick Model
• Subharmonic spin correlations and spectral pairing in Floquet time crystals
• Quasi-Discrete Time Crystals in the quasiperiodically driven Lipkin-Meshkov-Glick model
• Information scrambling and entanglement dynamics in Floquet Time Crystals
• On the Conditions for a Quantum Violent Relaxation
• Controlled bit-flip of period-doubling and discrete time crystalline states in open systems
• Stabilizing boundary time crystals through Non-markovian dynamics