Quantum many-body scars from magnon condensation

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 connected correlations in both space and time. We verify numerically the presence of this spatiotemporal long-range order and explain how it is consistent with established no-go theorems precluding its existence in ground states and at thermal equilibrium.