Classification of Non-Interacting Quantum Baths: Reconstruction of the Influence Matrix from Keldysh Correlation Functions

The recently developed influence matrix (IM) approach has opened new opportunities for the efficient simulation of quantum many-body dynamics in the thermalising and localised regimes. This approach is based on the Feynman-Vernon influence functional, which encodes the dynamical influence of a many-body bath on its local subsystems.

While a self-consistent approach to the computation of the IM using tensor-network techniques has proven to be versatile and efficient, a deeper analytical insight into the structure of IM is desirable to describe and classify quantum many body baths. In this talk, I will present a complementary perspective in which the IM is viewed as generating functional for Keldysh correlation functions. By computing these correlation functions explicitly, we reconstruct the IM for generic non-interacting systems of fermions. We will discuss the entanglement scaling of IM, as well as the dynamical properties of the resulting bath depending on the fermions spectral properties.