# Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation

## TL;DR

This paper links quantum many-body scarred eigenstates in a spin chain to magnon condensates, revealing space-time crystalline order and spontaneous time-translation symmetry breaking, supported by numerical evidence.

## Contribution

It introduces a novel interpretation of scarred eigenstates as magnon condensates, connecting nonergodic behavior with long-range space-time order in a nonintegrable spin chain.

## Key findings

- Scarred eigenstates are well-described by magnon condensates.
- Presence of long-range space-time crystalline order.
- Consistency with no-go theorems for equilibrium states.

## Abstract

We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body oscillations were observed only when the system was initialized in a particular product state. This pronounced coherence has been attributed to the presence of special "scarred" eigenstates with nearly equally-spaced energies and putative nonergodic properties despite their finite energy density. In this paper we uncover a surprising connection between these scarred eigenstates and low-lying quasiparticle excitations of the spin chain. In particular, we show that these eigenstates can be accurately captured by a set of variational states containing a macroscopic number of magnons with momentum $\pi$. This leads to an interpretation of the scarred eigenstates as finite-energy-density condensates of weakly interacting $\pi$-magnons. One natural consequence of this interpretation is that the scarred eigenstates possess long-range order in both space and time, providing a rare example of the spontaneous breaking of continuous time-translation symmetry. We verify numerically the presence of this space-time crystalline order and explain how it is consistent with established no-go theorems precluding its existence in ground states and at thermal equilibrium.