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

Abstract

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.

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• Quasi-Lindblad pseudomode theory for open quantum systems
• Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model
• Efficient construction of the Feynman-Vernon influence functional as matrix product states
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Efficient Pseudomode Representation and Complexity of Quantum Impurity Models
• Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems
• Unraveling screening mechanisms in Kondo impurities using an NRG-MPS-based method
• Scalable tensor network algorithm for quantum impurity problems
• Process Tensor Approaches to Non-Markovian Quantum Dynamics