Scar states in a system of interacting chiral fermions



I. Martin, K. A. Matveev


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.



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?
bunimovich_stadium.gif 2.67 MB


thank you for your question. Indeed, there is a connection with the "single-body" scar states that you describe.  The classical (unstable) periodic trajectories in billiards, when quantized, become quantum eigenstates with almost equal energy spacing and weight concentrated near the classical trajectory. They can be used to form wave packets that in semiclassical limit approximate the classical periodic trajectories.  In the many-body case, the scar states also form "towers" of equidistant in energy states. Moreover, their entaglement entropy is atypically low (compared to other states near their energy), making them in that sense more "classical". These two key similarities are the reason that the term "scar" was extended from single particle physics to many-body setting.

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