Real-Space Renormalization-Group Study of Decoherence and Revival Following a Sudden Quench in a Finite System

To investigate the nonequilibrium dynamics of a quantum impurity system, we examine two physical properties for the spinless resonant level model subject to sudden quenches of the hybridization between the impurity and the metal. We compute the time dependence of the impurity occupation and the survival probability (fidelity) as probes of the dephasing induced by particle-hole excitations. This dephasing reflects the entanglement between the impurity level and the metallic bath and, together with the loss of purity of this level, provides clear evidence of the loss of coherence, as discussed by Franco and Appel. For finite systems, coherence loss is only apparent, because discrete spectra lead to quasi-periodic dynamics and revivals when phases realign. We show that a hybrid linear–logarithmic discretization suppresses these finite-size artifacts by making the excitation energies incommensurate, thereby reducing revivals. Starting from the Rabi oscillations in the single-site limit of the tight-binding model describing the metal, we extend the analysis to large lattices, where damping and relaxation emerge. Our combination of analytical and numerical results offers a unified picture of the crossover from coherent oscillations to effectively irreversible decoherence.