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 (78)

• Quantum Computing in the NISQ era and beyond
• Quantum Cryptography
• Advances in Quantum Metrology
• Thermalization and its mechanism for generic isolated quantum systems
• Quantum information with Rydberg atoms
• Nonequilibrium dynamics of closed interacting quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• The physics of dipolar bosonic quantum gases
• Quantum computing with trapped ions
• Observation of a Discrete Time Crystal
• Quantum thermalization through entanglement in an isolated many-body system
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Floquet Time Crystals
• Cold atoms in cavity-generated dynamical optical potentials
• On the phase structure of driven quantum systems
• Quantum Time Crystals
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Dynamical quantum phase transitions: a review
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Quantum chaos challenges many-body localization
• Stability and instability towards delocalization in MBL systems
• Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
• Modeling spontaneous breaking of time-translation symmetry
• Discrete Time Crystals
• Periodically Driving a Many-Body Localized Quantum System
• SLE for theoretical physicists
• Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Floquet time crystal in the Lipkin-Meshkov-Glick model
• Dynamical obstruction to localization in a disordered spin chain
• Distinguishing localization from chaos: challenges in finite-size systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• A Guide to Stochastic Loewner Evolution and its Applications
• Conformally Invariant Fractals and Potential Theory
• Cryogenic Trapped-Ion System for Large Scale Quantum Simulation
• Markovian baths and quantum avalanches
• Quantum quenches, dynamical transitions and off-equilibrium quantum criticality
• Dynamical transitions and quantum quenches in mean-field models
• Finite speed of quantum scrambling with long range interactions
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Floquet time crystals in clock models
• A constructive theory of the numerically accessible many-body localized to thermal crossover
• Long-Range Prethermal Phases of Nonequilibrium Matter
• Higher-order and fractional discrete time crystals in clean long-range interacting systems
• Hierarchy of linear light cones with long-range interactions
• Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains
• Is there slow particle transport in the MBL phase?
• Dynamical critical scaling of long-range interacting quantum magnets
• Time crystals: analysis of experimental conditions
• Chaotic dynamical ferromagnetic phase induced by non-equilibrium quantum fluctuations
• Thermalization of dilute impurities in one dimensional spin chains
• Lifetime of almost strong edge-mode operators in one dimensional, interacting, symmetry protected topological phases
• Information propagation and equilibration in long-range Kitaev chains
• Metastability and discrete spectrum of long-range systems
• Quasiparticle origin of dynamical quantum phase transitions
• New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions
• Discrete time-crystalline response stabilized by domain-wall confinement
• Prethermal quantum many-body Kapitza phases of periodically driven spin systems
• Exact Multifractal Spectra for Arbitrary Laplacian Random Walks
• Almost strong 0, π edge modes in clean, interacting 1D Floquet systems
• Emergent parametric resonances and time-crystal phases in driven BCS systems
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Universal dynamical scaling of long-range topological superconductors
• Universal equilibrium scaling functions at short times after a quench
• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• The Poincare-Birkhoff theorem in Quantum Mechanics
• 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

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• 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
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• Quasi-Discrete Time Crystals in the quasiperiodically driven Lipkin-Meshkov-Glick model
• Information scrambling and entanglement dynamics in Floquet Time Crystals
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• Stabilizing boundary time crystals through Non-markovian dynamics