Tensor network influence functionals in the continuous-time limit: Connections to quantum embedding, bath discretization, and higher-order time propagation

We describe two developments of tensor network influence functionals (in particular, influence functional matrix product states (IF-MPS)) for quantum impurity dynamics within the fermionic setting of the Anderson impurity model.The first provides the correct extension of the IF-MPS to continuous time by introducing a related mathematical object, the boundary influence functional MPS.The second connects the dynamics described by a compressed IF-MPS to that of a quantum embedding method with a time-dependent effective bath undergoing nonunitary dynamics.Using these concepts, we implement higher-order time propagators for the quench dynamics of the Anderson impurity model within the boundary IF-MPS formalism.The calculations illustrate the ability of the current formulation to efficiently remove the time step error in standard discrete-time IF-MPS implementations as well as to interface with state vector propagation techniques.They also show the advantages of IF-MPS dynamics, with its associated highly compact effective bath dynamics, over state vector propagation with a static bath discretization.