Nonequilibrium quantum impurity problems via matrix-product states in the temporal domain

Describing a quantum impurity coupled to one or more non-interacting fermionic reservoirs is paradigmatic problem in many-body physics. While historically the focus has been on equilibrium properties of impurity-reservoir system, recent experiments with mesoscopic and cold-atomic systems enabled studies highly non-equilibrium models, which require novel theoretical techniques. We propose an approach analyze dynamics based matrix-product state (MPS) representation Feynman-Vernon influence functional (IF). The efficiency such MPS rests moderate value temporal entanglement (TE) entropy IF, viewed as fictitious "wave function" time domain. obtain explicit expressions this wave function for family one-dimensional reservoirs, scaling TE evolution different reservoir's initial states. states short-range correlations we find area-law scaling, Fermi-sea-type yield logarithmic time, closely related real-space critical 1d systems. Furthermore, describe efficient algorithm converting form reservoirs' IF form. Once encoded by MPS, arbitrary correlation functions interacting can be efficiently computed, irrespective its internal structure. introduced here applied number experimental setups, including transport via dots real-time formation correlations.