The time-evolving matrix product operator (TEMPO) method has become a very competitive numerical method for studying the real-time dynamics of quantum impurity problems. For small impurities, the most challenging calculation in TEMPO is to construct the matrix product state representation of the Feynman-Vernon influence functional. In this work we propose an efficient method for this task, which exploits the time-translationally invariant property of the influence functional. The required number of matrix product state multiplication in our method is almost independent of the total evolution time, as compared to the method originally used in TEMPO which requires a linearly scaling number of multiplications. The accuracy and efficiency of this method are demonstrated for the Toulouse model and the single impurity Anderson model.
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Author comments upon resubmission
We thank the editors and referee for the reports. We have revised our manuscript according to the referee's comments, and the reply to the report is given in the submission page. We hope that we have significantly improved the manuscript and answered the referee's questions properly.
List of changes
1. Added some descriptive sentences according to the referee's comments 2. Added an appendix about multiplication of GMPS 3. Added some discussion about the relation between the Prony method and linear prediction method
