Quantum many-body scars from unstable periodic orbits

Unstable periodic orbits (UPOs) play a key role in the theory of chaos, and scar the eigenstates of the corresponding quantum system. Recently, nonthermal many-body eigenstates embedded in an otherwise thermal spectrum have been identified as a many-body generalization of quantum scars. These many-body states, however, are not clearly associated to a chaotic phase space, and the connection between the single- and many-body notions of quantum scars remains therefore incomplete. Here, we find quantum many-body scars originating from UPOs in a chaotic phase space. Remarkably, these states verify the eigenstate thermalization hypothesis, due to high quantum instability, earning the name thermal quantum many-body scars. While they do not prevent thermalization, their spectral structure featuring approximately equispaced towers of states yields an anomalous oscillatory dynamics preceding thermalization for wavepackets initialized on an UPO. Remarkably, our model hosts both types of scars, thermal and nonthermal, and allows to study the crossover between the two. We show that the interplay of classical and quantum stability hints at a classification of quantum many-body scars. Our work illustrates the fundamental principle of classical-quantum correspondence in a many-body system, and its limitations.