# Floquet Time Spirals and Stable Discrete Time Quasi-Crystals in Quasi-Periodically Driven Quantum Many-Body Systems

## TL;DR

This paper explores quasi-periodically driven quantum systems, revealing Floquet Time Spirals and stable discrete time quasi-crystals that resist heating and break time-translation symmetry, extending understanding of non-equilibrium quantum phases.

## Contribution

It introduces the concept of Floquet Time Spirals and demonstrates the existence of stable discrete time quasi-crystals in many-body localized systems under quasi-periodic driving.

## Key findings

- Discovery of Floquet Time Spirals in quantum systems
- Existence of stable discrete time quasi-crystals
- Persistence of non-heating behavior under perturbations

## Abstract

We analyse quasi-periodically driven quantum systems that can be mapped exactly to periodically driven ones and find Floquet Time Spirals in analogy with spatially incommensurate spiral magnetic states. Generalising the mechanism to many-body systems we discover that a form of discrete time-translation symmetry breaking can also occur in quasi-periodically driven systems. We construct a discrete time quasi-crystal stabilised by many-body localisation. Crucially, it persists also under perturbations that break the equivalence with periodic systems. As such it provides evidence of a stable quasi-periodically driven many-body quantum system which does not heat up to the featureless infinite temperature state.