The accurate simulation of non-equilibrium quantum many-body dynamics is crucial in several domains, including quantum information, the study of thermalization, and impurity physics. However, the exponential number of parameters needed to describe many-body wavefunctions typically prevents exact computations for sizable systems. If their entanglement is low, wavefunctions can be approximated with relatively few parameters using matrix product states. Since equilibrium wavefunctions have low entanglement, this makes computations viable. However, when simulating dynamics, entanglement grows rapidly with the evolution time. In this talk, we explore a novel method for analyzing quantum many-body dynamics, inspired by the study of open quantum systems. We consider dynamics of a subsystem and view the rest of the many-body system as a bath.
The bath's properties are encoded in the influence functional (IF) on the space of Schwinger-Keldysh trajectories.
Treating the IF as a "wave function" in the temporal domain, we introduced the concept of Temporal Entanglement (TE) which can be interpreted as the "quantum memory" of the bath. For free fermionic bathts, we demonstrate that temporal entanglement scales favorably. We outline a strategy for efficiently representing the IF as a matrix product state in the temporal domain. This allows for the analysis of interacting quantum impurity dynamics through standard tensor contraction techniques. We then connect this problem to the larger context of generic quantum many-dynamics and outline aspects of this approach.