Eigenstate thermalization and disappearance of quantum many-body scar states in interacting fermion systems

TL;DR

This paper analytically demonstrates that quantum many-body scar states with low entanglement entropy vanish in interacting fermion systems, explaining their disappearance when interactions are introduced.

Contribution

It provides a quantitative, analytical proof that scar states are eliminated in interacting fermion systems, extending understanding of thermalization.

Findings

Scar states with sub-volume entanglement decay double exponentially with system size.

Weak interactions cause the probability of scar states to vanish rapidly.

Scar states are inherently unstable under generic interactions.

Abstract

The recent discovery of quantum many-body scar states has revealed the possibility of having states with low entanglement that violate the eigenstate thermalization hypothesis in nonintegrable systems. Such states with low entanglement entropy are rare but naturally exist in the integrable system of free fermions. Here, we demonstrate analytically that these atypical states would be always eliminated when an arbitrary weak interaction is introduced between the fermions. In particular, we show that the probability of having a many-body scar state with entanglement entropy satisfying a sub-volume scaling law decreases double exponentially as the system size. Thus, our results provide a quantitative argument for the disappearance of scar states in interacting fermion systems.