# Integrable Floquet dynamics

## TL;DR

This paper explores classes of integrable Floquet systems that resist chaos under periodic driving, introducing new models like boost models and demonstrating potential for experimental realization and novel oscillating states.

## Contribution

It introduces the concept of boost models in integrable Floquet systems and explores their properties, including the generation of oscillating states called 'Quantum Boost Clocks.'

## Key findings

- Identification of three classes of integrable Floquet systems.
- Construction of boost models as periodic interchange of Hamiltonians.
- Proposal of experimental realization and observation of oscillating states.

## Abstract

We discuss several classes of integrable Floquet systems, i.e. systems which do not exhibit chaotic behavior even under a time dependent perturbation. The first class is associated with finite-dimensional Lie groups and infinite-dimensional generalization thereof. The second class is related to the row transfer matrices of the 2D statistical mechanics models. The third class of models, called here "boost models", is constructed as a periodic interchange of two Hamiltonians - one is the integrable lattice model Hamiltonian, while the second is the boost operator. The latter for known cases coincides with the entanglement Hamiltonian and is closely related to the corner transfer matrix of the corresponding 2D statistical models. We present several explicit examples. As an interesting application of the boost models we discuss a possibility of generating periodically oscillating states with the period different from that of the driving field. In particular, one can realize an oscillating state by performing a static quench to a boost operator. We term this state a "Quantum Boost Clock". All analyzed setups can be readily realized experimentally, for example in cod atoms.