ScarFinder: a detector of optimal scar trajectories in quantum many-body dynamics (2504.12383v1)

Abstract: Mechanisms that give rise to coherent quantum dynamics, such as quantum many-body scars, have recently attracted much interest as a way of controlling quantum chaos. However, identifying the presence of quantum scars in general many-body Hamiltonians remains an outstanding challenge. Here we introduce ScarFinder, a variational framework that reveals possible scar-like dynamics without prior knowledge of scar states or their algebraic structure. By iteratively evolving and projecting states within a low-entanglement variational manifold, ScarFinder isolates scarred trajectories by suppressing thermal contributions. We validate the method on the analytically tractable spin-1 XY model, recovering the known scar dynamics, as well as the mixed field Ising model, where we capture and generalize the initial conditions previously associated with ``weak thermalization''. We then apply the method to the PXP model of Rydberg atom arrays, efficiently characterizing its mixed phase space and finding a previously unknown trajectory with nearly-perfect revival dynamics in the thermodynamic limit. Our results establish ScarFinder as a powerful, model-agnostic tool for identifying and optimizing coherent dynamics in quantum many-body systems.

Overview of "ScarFinder: a detector of optimal scar trajectories in quantum many-body dynamics"

This paper introduces ScarFinder, a variational framework designed to identify scar-like dynamics within quantum many-body systems without prior knowledge of scar states or their algebraic structures. Quantum many-body scars (QMBS) are nonthermal eigenstates that defy the eigenstate thermalization hypothesis (ETH), exhibiting atypical dynamics such as slow entanglement growth and periodic revivals. ScarFinder aims to uncover these dynamics in general Hamiltonians that lack integrability or conserved quantities, which makes analytical treatment challenging.

Methodology

ScarFinder operates by iteratively evolving and projecting states within a low-entanglement variational manifold, such as matrix product states (MPS), capable of supporting low-entanglement dynamics. The algorithm suppresses thermal contributions to isolate scar trajectories by the following steps:

1. Evolution: The system is evolved under the Hamiltonian over a time interval $\Delta t$.
2. Projection: The evolved state is projected back onto the variational manifold, reducing the buildup of entanglement associated with thermal states.
3. Optimization: This process is iteratively repeated to converge towards periodic trajectories within the manifold.

Case Studies

The paper validates ScarFinder on the spin-1 XY model, capturing known scar dynamics in analytically tractable settings. Furthermore, ScarFinder is applied to the PXP model of Rydberg atom arrays, where it identifies a previously unknown scar trajectory that exhibits close-to-perfect revivals in the thermodynamic limit.

Numerical Experiments

ScarFinder's convergence depends on the choice of projection time $\Delta t$ and the state relevance within the scar subspace. Larger $\Delta t$ generally aids in distinguishing scar from thermal components, resulting in faster convergence for states initially far from scar trajectories. The study has demonstrated that ScarFinder reliably identifies optimal scar states even with a small number of initial trials.

Implications

ScarFinder offers a model-agnostic approach for identifying coherent dynamics in chaotic quantum systems, providing insights into spectrally isolated nonthermal eigenstates. The framework's ability to operate efficiently in the thermodynamic limit makes it particularly useful for large-scale quantum simulations and the study of quantum chaos.

Future Prospects

The development of ScarFinder invites further exploration into model-specific modifications and the search for scars in higher-dimensional quantum systems. Additionally, it highlights potential avenues for experimental validation of identified scar states through quantum simulation platforms.

Conclusion

ScarFinder stands as a powerful tool for probing nonthermal dynamics within many-body quantum systems, contributing significantly to the understanding of QMBS and their implications for quantum information processing and the study of complex quantum phenomena. The framework establishes a foundation for future theoretical and practical advancements in identifying and controlling quantum scars.