Observing Quantum Phases and Multiparticle Entanglement Dynamics in a Central Qudit Ising Model

Quantum spin models are host to interesting phenomena including criticality and novel dynamical response. Detecting and understanding these phases as well as the underlying fluctuations and more importantly entanglement physics, is a long-standing issue. Through the use of an ancillary central qudit coupled to the paradigmatic transverse Ising model, we show how simple probes on the external ancilla provide details about the ground state and non-equilibrium phase of the system as well as how the phases are modified by this nonintegrable coupling. More interstingly, we observe that the development of fluctuations that captures mulitparticle entanglement in the pure Ising system also quantifies how entanglement and correlations serve to thermalize this composite system. Our findings are robust to the environment Hilbert space and physical couplings between spins and ancilla.