# The fate of a discrete time crystal in an open system

## TL;DR

This paper investigates the stability of discrete time crystals in disordered one-dimensional quantum systems when coupled to an external environment, showing that such coupling destroys the DTC phase over time.

## Contribution

It provides analytical and numerical evidence that environmental coupling destabilizes discrete time crystals in one-dimensional disordered systems.

## Key findings

- DTCs are destroyed at long times due to environmental coupling.
- The destruction occurs even when the system is protected from heating.
- Disorder does not prevent the loss of DTC order in open systems.

## Abstract

Following the recent realisation that periodically driven quantum matter can support new types of spatiotemporal order, now known as discrete time crystals (DTCs), we consider the stability of this phenomenon. Motivated by its conceptual importance as well as its experimental relevance we consider the effect of coupling to an external environment. We use this to argue, both analytically and numerically, that the DTC in disordered one-dimensional systems is destroyed at long times by any such natural coupling. This holds true even in the case where the coupling is such that the system is prevented from heating up by an external thermal bath.