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

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.