Complexity and Floquet dynamics: non-equilibrium Ising phase transitions

Abstract

We study the time-dependent circuit complexity of the periodically driven transverse field Ising model using Nielsen's geometric approach. In the high-frequency driving limit the system is known to exhibit non-equilibrium phase transitions governed by the amplitude of the driving field. We analytically compute the complexity in this regime and show that it clearly distinguishes between the different phases, exhibiting a universal linear behavior at early times. We also evaluate the time averaged complexity, provide evidence of non-analytic behavior at the critical points, and discuss its origin. Finally, we comment on the freezing of quantum dynamics at specific configurations and on the use of complexity as a new tool to understand quantum phase transitions in Floquet systems.

8 pages, 4 figures

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Cited by in corpus (10)

• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Complexity for Conformal Field Theories in General Dimensions
• Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
• Integrable Quantum Circuits from the Star-Triangle Relation
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Hilbert-Space Ergodicity in Driven Quantum Systems: Obstructions and Designs
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity
• Time-dependent Hamiltonians and Geometry of Operators Generated by Them
• Emergence of prethermal time quasicrystalline order in a quasiperiodically driven non-interacting spin chain
• Quantum dynamics of a spin model with an extensive degeneracy