A Universal Model of Floquet Operator Krylov Space

Abstract

It is shown that the stroboscopic time-evolution under a Floquet unitary, in any spatial dimension, and of any Hermitian operator, can be mapped to an operator Krylov space which is identical to that generated by the edge operator of the non-interacting Floquet transverse-field Ising model (TFIM) in one-spatial dimension, and with inhomogeneous Ising and transverse field couplings. The latter has four topological phases reflected by the absence (topologically trivial) or presence (topologically non-trivial) of edge modes at $0$ and/or $\pi$ quasi-energies. It is shown that the Floquet dynamics share certain universal features characterized by how the Krylov parameters vary in the topological phase diagram of the Floquet TFIM with homogeneous couplings. These results are highlighted through examples, all chosen for numerical convenience to be in one spatial dimension: non-integrable Floquet spin $1/2$ chains and Floquet $Z_3$ clock model where the latter hosts period-tripled edge modes.

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Cited by in corpus (8)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators
• Streamlined Krylov construction and classification of ergodic Floquet systems
• Duality defect in a deformed transverse-field Ising model
• Opening Krylov space to access all-time dynamics via dynamical symmetries
• Moment method and continued fraction expansion in Floquet Operator Krylov Space
• Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures
• Floquet operator dynamics and orthogonal polynomials on the unit circle