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

TL;DR

This paper introduces a Floquet protocol for generating long-range entanglement in a generalized quantum Potts model, specifically for qutrits, and suggests its integrability with potential experimental realizations.

Contribution

The paper proposes a novel Floquet protocol for entanglement in the quantum Potts model and demonstrates its integrability through algebraic constructions linked to the Temperley-Lieb algebra.

Findings

Protocol creates long-range entangled qutrit pairs.

Conjecture and partial proof of Floquet integrability.

Results applicable to experimental quantum simulators.

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 non-local 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 non-trivial 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.