Quantum many-body scars (1711.03528v2)

Abstract: Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" 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.

• The paper identifies many-body quantum scars as special eigenstates that defy conventional thermalization in Fibonacci chain models.
• The study employs theoretical modeling and Rydberg atom experiments to demonstrate coherent oscillations and non-ergodic dynamics.
• The work challenges the eigenstate thermalization hypothesis and suggests a new universality class in quantum many-body systems.

Quantum Many-Body Scars: Insights and Implications

The paper "Quantum many-body scars," authored by C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi ć, introduces the concept of many-body quantum scars within the context of non-ergodic dynamics in quantum systems. This research contributes to our understanding of quantum dynamics in kinetically-constrained one-dimensional (1D) models, specifically focusing on the Fibonacci chain realized in Rydberg atom quantum simulators.

Overview and Key Contributions

The authors explore quantum many-body scars as representing special eigenstates that are concentrated in particular regions of the Hilbert space. These states deviate from the typical behavior expected in thermalizing dynamics by persistently contributing to non-ergodic phenomena. The paper particularly investigates the scarred wave functions in the Fibonacci chain, a model that is both theoretically intriguing and experimentally realizable through Rydberg atom setups. Here are the primary elements of this investigation:

1. Definition and Identification of Scars: Initially recognized in single-particle quantum chaotic systems, quantum scars are wave functions concentrated along classical periodic orbits. Extending this concept, the paper identifies many-body quantum scars as special eigenstates within the spectrum of 1D systems, specifically those with constrained local Hilbert spaces.
2. Modeling with a Fibonacci Chain: The research considers the Fibonacci chain—an effective model for anyonic excitations in two-dimensional topological phases—demonstrating that this system exhibits quantum many-body scars. The choice of the Fibonacci chain is due to its intriguing properties: the constrained Hilbert space grows following the Fibonacci sequence, and it challenges conventional thermalization behaviors by embedding scarred states throughout the many-body spectrum.
3. Experimental Signatures and Theoretical Modeling: These scarred eigenstates are shown to manifest experimentally through coherent oscillations upon quenching from a charge-density wave state. The team presents a model based on a single particle hopping on a Hilbert space graph, effectively describing these special states for relatively large systems.
4. Potential New Universality Class: The existence of scarred many-body bands suggests the possibility of a new universality class for quantum dynamics that is neither fully ergodic nor locally constrained. This diverges from the existing classification involving integrable models or systems exhibiting many-body localization (MBL).

Implications and Future Directions

Theoretical Implications: The findings propose that many-body quantum scars could challenge the eigenstate thermalization hypothesis (ETH), which posits that isolated quantum systems evolve towards thermal equilibrium. The observation of scars suggests that certain many-body eigenstates can evade thermalization, fundamentally impacting our understanding of quantum statistical mechanics.

Experimental Realizability: The realization of such models in current experimental settings—notably Rydberg atom setups—opens pathways for conducting real-time dynamic studies that may further elucidate the properties and behaviors of quantum many-body scars in larger and more complex systems.

Potential Applications: Given their non-thermalizing dynamics, scarred states have implications for quantum information processing and storage, where coherent oscillations can be harnessed for prolonged times.

Research Challenges: Open questions remain concerning the identification and classification of these special states across different models. Expanding the paper to include other constrained models may aid in understanding the common properties leading to such non-ergodic behavior.

Future Developments: Further research could explore whether similar scar phenomena occur in higher-dimensional systems, and how external perturbations or parameter variations influence the preservation of these scars.

In conclusion, this contribution provides an insightful exploration of many-body quantum scars and sets the stage for expansive research in non-ergodic quantum dynamics, with promising experimental and theoretical avenues to explore.