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arXiv:2110.09559 · Physical review. B./Physical review. B

Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model

Anatoliy I. Lotkov, Vladimir Gritsev, Aleksey K. Fedorov, Denis V. Kurlov

Published Apr 28, 2022• 13 citations
arXivHTMLPDF

Abstract

We develop a Floquet protocol for long-range entanglement generation in the one-dimensional quantum Potts model, which generalizes the transverse-filed Ising model by allowing each spin to have $n>2$ states. We focus on the case of $n=3$, so that the model describes a chain of qutrits. The suggested protocol creates qutrit Bell-like pairs with nonlocal long-range entanglement that spans over the entire chain. We then conjecture that the proposed Floquet protocol is integrable and explicitly construct a few first nontrivial conserved quantities that commute with the stroboscopic evolution operator. Our analysis of the Floquet integrability relies on the deep connection between the quantum Potts model and a much broader class of models described by the Temperley-Lieb algebra. We work at the purely algebraic level and our results on Floquet integrability are valid for any representation of the Temperley-Lieb algebra. We expect that our findings can be probed with present experimental facilities using Rydberg programmable quantum simulators and can find various applications in quantum technologies.

DOI
10.1103/physrevb.105.144306

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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 1/21/21/2 chains and Floquet Z3{Z}_{3}Z3​ clock model where the latter hosts period-tripled edge modes.