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.

Supplemental material is divided into three sections. The first section provides additional data that supports the argument in the main text. The second section describes a super-fermion representation in more detail with explicit constructions. The third section explains the technical details of how to evaluate the quantity of 1-RDM in the main text.