# Periodically driven random quantum spin chains : Real-Space Renormalization for Floquet localized phases

## TL;DR

This paper introduces a real-space renormalization method for analyzing Floquet localized phases in periodically driven random quantum spin chains, extending existing techniques to handle time-dependent dynamics.

## Contribution

It proposes a Block-self-dual renormalization procedure for constructing localized eigenstates in Floquet systems, generalizing the Strong Disorder Renormalization approach.

## Key findings

- Developed a renormalization method for Floquet localized phases
- Extended RSRG-X to time-dependent Floquet systems
- Provided a framework for eigenstate construction in driven disordered chains

## Abstract

When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a Block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding Strong Disorder Renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.