Revivals imply quantum many-body scars

TL;DR

This paper establishes a fundamental link between perfect quantum revivals in many-body systems and the existence of special eigenstates called quantum many-body scars, characterized by specific entanglement properties and energy structure.

Contribution

It proves that revivals necessarily imply the presence of quantum many-body scars with particular entanglement and energy characteristics, providing a general theoretical framework.

Findings

Perfect revivals imply quantum many-body scars with specific entanglement properties.

Quantum many-body scars are necessary for revivals, regardless of Hamiltonian details.

Revivals of states become increasingly short-lived as system size grows.

Abstract

We derive general results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time at most poly(N) implies the existence of "quantum many-body scars", whose number grows at least as the square root of N up to poly-logarithmic factors. These are energy eigenstates with energies placed in an equally-spaced ladder and with R\'enyi entanglement entropy scaling as log(N) plus an area law term for any region of the lattice. This shows that quantum many-body scars are a necessary condition for revivals, independent of particularities of the Hamiltonian leading to them. We also present results for approximate revivals, for revivals of expectation values of observables and prove that the duration of revivals of states has to become vanishingly short with increasing system size.