Dmitry ABANIN
Dynamical properties of a many-body system are determined by its properties as a quantum bath: the systems that thermalize act as an efficient bath, while integrable and many-body localized (MBL) systems fail to do so. I will describe a new approach to quantum many-body dynamics, inspired by the notion of the Feynman-Vernon influence functional (IF), which captures the properties of a quantum bath. I will consider interacting spin systems, and formulate an equation satisfied by their influence functionals. Surprisingly, this equation can be solved exactly for a class of many-body systems – perfect dephasers – which act as Markovian baths on their subsystems. More generally, I will show that, viewed as a fictitious wave function in the temporal domain, influence functional can be described by tensor-network methods. The efficiency of this approach is based on the behavior of temporal entanglement of the IF — a quantity that I will introduce — which remains low in very different physical regimes, including fast thermalization, integrability, and many-body localization. I will also discuss applications of this approach in the context of recent quantum simulation experiments, where the method allowed an efficient description of dissipation effects. IF approach offers a new lens on many-body non-equilibrium phenomena, both in ergodic and non-ergodic regimes, connecting the theory of open quantum systems to quantum statistical physics.
[1] Lerose, Sonner, Abanin, Phys. Rev. X 11, 021040 (2021); arXiv:2012.00777; arXiv:2103.13741; arXiv:2104.07607