ScarFinder: A Detector of Optimal Scar Trajectories in Quantum Many-Body Dynamics

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 SF, a variational framework that reveals possible scar-like dynamics without prior knowledge of scar states or their algebraic structure, assuming only that such dynamics remain low in entanglement. By iteratively evolving and projecting states within a variational manifold, SF isolates scarred trajectories by suppressing thermal contributions. We validate the method on the analytically tractable spin-1 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>X</a:mi> <a:mi>Y</a:mi> </a:math> 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, finding a previously unknown trajectory with nearly-perfect revival dynamics in the thermodynamic limit. We also demonstrate that SF can efficiently identify the centers of stable islands in Poincaré sections of the mixed phase space that results from the projection of many-body quantum dynamics to a variational manifold. Our results establish SF as a powerful, model-agnostic tool for identifying and optimizing coherent dynamics in quantum many-body systems.