Two dimensional kicked quantum Ising model: dynamical phase transitions

Abstract

Using an efficient one and two qubit gate simulator, operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two dimensional lattice, which is periodically driven by a $\delta$-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density and (ii) level spacing distribution of the Floquet quasienergy spectrum, as well as (iii) time-averaged autocorrelation function of components of the magnetization. Varying the parameters of the model, we found transitions between ordered (non ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density {\em do not} correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found nice agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially noninteracting, even in the regions where local observables are not ergodic or where spectral density is non-flat. These findings put in question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality.

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Cited by in corpus (11)

• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum
• Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
• Heating in integrable time-periodic systems
• Loschmidt echo in many-spin systems: contrasting time-scales of local and global measurements
• Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility
• Periodically driven random quantum spin chains : Real-Space Renormalization for Floquet localized phases
• Stabilizing coherence with nested environments: a numerical study using kicked Ising models
• Corner transfer matrices for 2D strongly coupled many-body Floquet systems
• Unveiling clean two-dimensional discrete time crystals on a digital quantum computer
• Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices