Fractal nature of high-order time crystal phases
Guido Giachetti, Andrea Solfanelli, Lorenzo Correale, Nicolò Defenu
Abstract
In Floquet time crystals, characterized by the spontaneous breaking of time-translational invariance, observables exhibit oscillations with a period multiple $p>2$ of the driving. Here, a new, experimentally accessible, order parameter is introduced, able to detect time-crystalline phases regardless of the value of $p$. This unveils a rich landscape with self-similar fractal boundaries in the phase diagram of the long-range kicked Ising model. These features are explained within the theoretical framework, along with the emergence of the ${Z}_{p}$ symmetry in Bloch eigenstates.
Topics & Concepts
Floquet theoryFractalIsing modelPhysicsObservablePhase diagramOrder (exchange)Eigenvalues and eigenvectorsTranslational symmetryStatistical physicsSymmetry (geometry)Symmetry breakingPhase (matter)Quantum mechanicsTheoretical physicsCondensed matter physicsMathematicsGeometryMathematical analysisFinanceNonlinear systemEconomicsQuantum many-body systemsTheoretical and Computational PhysicsQuantum chaos and dynamical systems