Slow quench dynamics of the subsystem return probability across a quantum critical point

The Loschmidt Echo (LE), a measure of the probability for a quantum many-body state to return to itself under dynamical evolution, is experimentally inaccessible due to its exponential suppression with system size. Recent theoretical and experimental studies have investigated the sudden-quench dynamics of the experimentally accessible subsystem return probability (SRP), which quantifies the local return probability. Sudden quenching studies have shown that in the low-temperature limit, the SRP acts as a sensitive probe of the quantum critical point, while in the high-temperature limit it reflects the thermodynamic entropy of the subsystem. Here, we explore the SRP under slow quenches across the critical point, where the dynamics are near-adiabatic except near criticality, where the energy gap closes and Kibble–Zurek physics predicts the formation of defects which suppress the LE. Our results provide bounds on the fidelity of locally prepared states in annealing protocols and link the observed scaling behavior to the long-range correlations of bipartite subsystems. Our results are presented for the transverse-field Ising model (TFIM), with and without integrability-breaking terms.