# Integrable many-body quantum Floquet-Thouless pumps

## TL;DR

This paper introduces an exactly solvable interacting quantum Floquet model with topologically nontrivial quasiparticles, revealing new integrable structures and operator dynamics in periodically driven quantum systems.

## Contribution

It presents a novel integrable Floquet model with topological quasiparticles, solvable via simplified Bethe equations, and demonstrates unique operator spreading properties.

## Key findings

- Exact solution of the Bethe equations for the model
- Construction of operators with no butterfly effect
- Illustration of a new class of solvable Floquet quantum systems

## Abstract

We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model, and show that these take on a particularly simple form that allows for an exact solution: essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem to be possible in other interacting integrable systems. This model illustrates the existence a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.