Quantum Liang Information Flow Probe of Causality across Critical Points

Investigating causation in the quantum domain is crucial. Despite numerous studies of correlations in quantum many-body systems, causation, which is very distinct from correlations, has hardly been studied. We address this by demonstrating the efficacy of the newly established causation measure, quantum Liang information flow, in quantifying causality across phase diagrams of quantum many-body systems. We focus on quantum criticality, which are highly nonclassical points. We extract causation behavior across a spectrum-wide critical point and a ground state second-order phase transition in both integrable and nonintegrable systems. Across criticality, each case exhibits distinct hallmarks, different from correlation measures. We also deduce that quantum causation qualitatively follows the quasiparticle picture of information propagation in integrable systems but exhibits enhanced quantum nonlocality near criticality. At times significantly larger than the spatial separation, it extracts additional features from the equilibrium wave function, leading to a peak just before the critical point for near boundary sites.