January 5, 2024 | Cedric Lim, Kirill Matirko, Anatoli Polkovnikov, and Michael O. Flynn
The paper proposes a formalism to define chaos in both quantum and classical systems using adiabatic transformations. The complexity of these transformations, which preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations, serves as a measure of chaos. This complexity is quantified by the fidelity susceptibility, a quantity that characterizes the sensitivity of eigenstates to small perturbations. The authors demonstrate that this approach allows for the distinction between integrable, chaotic but non-thermalizing, and ergodic regimes. They apply the fidelity susceptibility to a model of two coupled spins, showing that it successfully predicts the universal onset of chaos in both finite spin and the classical limit. Interestingly, they find that finite spin effects are anomalously large close to integrability. The paper also discusses the connection between operator growth and spectral functions, and provides a detailed analysis of the spectral function and fidelity susceptibility for the model Hamiltonian.The paper proposes a formalism to define chaos in both quantum and classical systems using adiabatic transformations. The complexity of these transformations, which preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations, serves as a measure of chaos. This complexity is quantified by the fidelity susceptibility, a quantity that characterizes the sensitivity of eigenstates to small perturbations. The authors demonstrate that this approach allows for the distinction between integrable, chaotic but non-thermalizing, and ergodic regimes. They apply the fidelity susceptibility to a model of two coupled spins, showing that it successfully predicts the universal onset of chaos in both finite spin and the classical limit. Interestingly, they find that finite spin effects are anomalously large close to integrability. The paper also discusses the connection between operator growth and spectral functions, and provides a detailed analysis of the spectral function and fidelity susceptibility for the model Hamiltonian.