Quantum many-body scars

TLDR

Quantum scarred wave functions in non‑interacting chaotic systems concentrate near unstable periodic classical trajectories, revealing special structures in their real‑space density profiles. The paper introduces many‑body quantum scars, a subset of special eigenstates concentrated in specific Hilbert‑space regions. They model scars as a single particle hopping on a Hilbert‑space graph, accurately reproducing scarred wave functions up to 32 atoms. Scars are found in the Fibonacci chain, producing robust oscillations after a charge‑density‑wave quench and suggesting a new universality class of quantum dynamics with long‑lived coherence.

Abstract

Certain wave functions of non-interacting quantum chaotic systems can exhibit in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.