# Ballistic spin transport in a periodically driven integrable quantum system

## TL;DR

This paper demonstrates ballistic spin transport in a periodically driven integrable quantum system, revealing a fractal lower bound on the spin Drude weight and providing insights into quantum transport in Floquet spin chains.

## Contribution

It introduces an analytic family of quasi-local conservation laws for a Floquet spin chain and establishes a fractal lower bound on the spin Drude weight.

## Key findings

- Ballistic spin transport observed in the model.
- Fractal dependence of the lower bound on anisotropy.
- Numerical simulations support the tightness of the bound.

## Abstract

We demonstrate ballistic spin transport of an integrable unitary quantum circuit, which can be understood either as a paradigm of an integrable periodically driven (Floquet) spin chain, or as a Trotterized anisotropic ($XXZ$) Heisenberg spin-1/2 model. We construct an analytic family of quasi-local conservation laws that break the spin-reversal symmetry and compute a lower bound on the spin Drude weight which is found to be a fractal function of the anisotropy parameter. Extensive numerical simulations of spin transport suggest that this fractal lower bound is in fact tight.