Universal model of Floquet operator Krylov space
Hsiu-Chung Yeh, Aditi Mitra
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 noninteracting 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 nontrivial) of edge modes at 0 and/or $\ensuremath{\pi}$ quasienergies. 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: nonintegrable Floquet spin $1/2$ chains and Floquet ${Z}_{3}$ clock model where the latter hosts period-tripled edge modes.