Correspondence between quasiparticle dissipation and quantum information decay in open quantum systems

Diagrammatic techniques simplify a weakly interacting many-body problem into an effective few-quasiparticle problem within a system of interest (SOI). If scattering events, mediated by a bath, between those quasiparticles can be approximated as density-density interactions, the bath behaves like an effective external potential. On the other hand, exchange interactions could entangle those quasiparticles and the bath, leading to an open quantum system that induces quantum decoherence and spectral broadening. We investigate the renormalized interaction between the SOI and the bath, employing a projection operator technique similar to the one used in the Nakajima-Zwanzig method. We find that the frequency variation of this renormalized interaction is analogous to the quasiparticle residue and provides a measure of the SOI-bath separability that serves as the lower bound of the SOI-bath entanglement entropy. In the weak-coupling regime and continuum limit, we demonstrate that the degree of SOI-bath separability corresponds to the quasiparticle spectral weight in the single-impurity Anderson model and find that the loss of quantum information to the continuum of the bath can be understood as a decay process where an initial single-impurity state escapes to a thermal bath. This work provides a direction for connecting energy dissipation in quasiparticles propagation to the loss of quantum information in open quantum systems.