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

• URL: http://arxiv.org/abs/2401.12460v2
• Date: Tue, 2 Jul 2024 16:34:36 GMT
• Title: Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• Authors: Gunhee Park, Nathan Ng, David R. Reichman, Garnet Kin-Lic Chan,
• Abstract summary: We implement higher-order time propagators for the quench dynamics of the Anderson impurity model within the boundary IF-MPS formalism. We show the advantages of IF-MPS dynamics, with its associated highly compact effective bath dynamics, over state vector propagation with a static bath discretization.
• Score: 2.368662284133926
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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