# Critical Time Crystals in Dipolar Systems

## TL;DR

This paper investigates the stability and lifetime of discrete time crystalline order in 3D dipolar systems, revealing a critical regime stabilized by slow dynamics rather than localization, with implications for quantum matter probing.

## Contribution

It introduces a perturbative approach to evaluate DTC lifetime in dipolar systems and predicts a sharp crossover indicating a novel critical DTC regime.

## Key findings

- Decay of DTC order is parametrically slow in 3D dipolar systems.
- A sharp crossover from stable DTC to loss of order is predicted.
- Experimental results align with the theoretical predictions of a critical DTC regime.

## Abstract

We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature 543, 221-225 (2017)]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.