# The isolated Heisenberg magnet as a quantum time crystal

## TL;DR

This paper shows that the isolated Heisenberg XXZ spin chain can act as a genuine quantum time crystal, exhibiting persistent oscillations due to dynamical symmetries, without external driving or environment coupling.

## Contribution

It analytically and numerically demonstrates the existence of a quantum time crystal in an isolated Heisenberg magnet, highlighting the role of dynamical symmetries and their fractal dependence on anisotropy.

## Key findings

- The Heisenberg XXZ chain does not relax to stationarity.
- Persistent oscillations are caused by dynamical symmetries.
- Frequency of oscillations varies fractally with anisotropy.

## Abstract

We demonstrate analytically and numerically that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. We trace this phenomenon to the existence of extensive dynamical symmetries and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain. We discuss how the ensuing persistent oscillations that violate one of the most fundamental laws of physics could be observed experimentally and identify potential metrological applications.