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Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral

Xiansong Xu1,2, Chu Guo3, Ruofan Chen1

  • 1College of Physics and Electronic Engineering, and Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China.

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|October 15, 2024
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Summary
This summary is machine-generated.

We introduce a new numerical method, the Grassmann time-evolving matrix product operator method, for studying fermionic open quantum systems. This robust approach handles complex quantum dynamics and can serve as an impurity solver.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • Studying open quantum systems is challenging due to non-perturbative and non-Markovian dynamics.
  • The Feynman-Vernon influence functional approach is key for analytical studies.
  • Existing numerical methods work well for bosonic environments but struggle with fermionic systems.

Purpose of the Study:

  • To present the Grassmann time-evolving matrix product operator method for fermionic open quantum systems.
  • To introduce novel concepts like Grassmann tensors and operators for handling fermionic path integrals.
  • To demonstrate the method's utility with benchmarks on the Anderson impurity model.

Main Methods:

  • Developed the Grassmann time-evolving matrix product operator (G-TEMPO) method.
  • Introduced Grassmann tensors, signed matrix product operators, and Grassmann matrix product states.
  • Applied G-TEMPO to the single-orbital Anderson impurity model for various dynamics.

Main Results:

  • Successfully benchmarked the G-TEMPO method for real-time nonequilibrium and equilibration dynamics.
  • Demonstrated its capability as an impurity solver for fermionic open quantum systems.
  • Validated the method's robustness for strong coupling physics and non-Markovian dynamics.

Conclusions:

  • The G-TEMPO method is a robust and promising numerical approach for fermionic open quantum systems.
  • It effectively handles complex quantum dynamics, including strong coupling and non-Markovian effects.
  • It offers an alternative impurity solver for strongly correlated quantum matter within dynamical mean-field theory.