## Authors

I. Martin, K. A. Matveev

## Abstract

We study the nature of many-body eigenstates of a system of interacting chiral spinless fermions on a ring. We find a coexistence of fermionic and bosonic types of eigenstates in parts of the many-body spectrum. Some bosonic eigenstates, native to the strong interaction limit, persist at intermediate and weak couplings, enabling persistent density oscillations in the system, despite it being far from integrability.

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Question:

There is a notion of a quantum scar in conventional single-particle chaos. For example, consider the regular stadium billiard, like the picture below. Most classical trajectories are ergodic - cover the entire billiard. But there is a zero-measure set of trajectories - which just bounce back and forth between the two walls if you launch them exactly at 90 degrees. If you quantize, you'll see more or less random (in the sense of Berry) wave functions, but there will be some traces of the "non-ergodic" trajectories - these are what's usually called "scars" in single particle quantum chaos. Is the notion of a many-body scar related to it at all? What's the definition of a many-body scare?

There is a notion of a quantum scar in conventional single-particle chaos. For example, consider the regular stadium billiard, like the picture below. Most classical trajectories are ergodic - cover the entire billiard. But there is a zero-measure set of trajectories - which just bounce back and forth between the two walls if you launch them exactly at 90 degrees. If you quantize, you'll see more or less random (in the sense of Berry) wave functions, but there will be some traces of the "non-ergodic" trajectories - these are what's usually called "scars" in single particle quantum chaos. Is the notion of a many-body scar related to it at all? What's the definition of a many-body scare?