Universal model of Floquet operator Krylov space

Journal Article · 04 October 2024 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.110.155109 · OSTI ID:2454999

Yeh, Hsiu-Chung ^[1]; Mitra, Aditi  ^[2]

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1. New York University, NY (United States); New York University
2. New York University, NY (United States)

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 π 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. Furthermore, 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 Z₃ clock model where the latter hosts period-tripled edge modes.

• Research Organization: New York University, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0010821
• OSTI ID: 2454999
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 15 Vol. 110; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English