Holographic Quantum Scars

TL;DR

This paper constructs and analyzes quantum many-body scar states within holographic conformal field theories, revealing their unique non-thermal properties, periodic dynamics, and geometric duals related to empty AdS space.

Contribution

It introduces a novel holographic construction of quantum many-body scars using Virasoro symmetries and explores their geometric and entanglement properties.

Findings

Scarred states are non-thermal with unique entanglement entropy growth.

Holographic duals of scarred states relate to diffeomorphisms of empty AdS.

Entanglement entropy scales as log(E) for scarred states.

Abstract

We discuss a construction of quantum many-body scars in the context of holography. We consider two-dimensional conformal field theories and use their dynamical symmetries, naturally realized through the Virasoro algebra, to construct scarred states. By studying their Loschmidt amplitude, we evaluate the states' periodic properties. A geometrical interpretation allows us to compute the expectation value of the stress tensor and entanglement entropy of these scarred states. We show that their holographic dual is related by a diffeomorphism to empty AdS, even for energies above the black hole threshold. We also demonstrate that expectation values in the scarred states are generally non-thermal and that their entanglement entropy grows with the energy as $\log(E)$ in contrast to $\sqrt{E}$ for the typical (bulk) states. Furthermore, we identify fixed points on the CFT plane associated with divergent or vanishing entanglement entropy in the limit where the scarred states have infinite energy.