Stochastic equation of motion approach to fermionic dissipative dynamics. II. Numerical implementation.

Area of Science:

• Quantum Mechanics
• Computational Physics
• Condensed Matter Physics

Background:

• Open quantum systems are crucial for understanding energy and particle transport.
• Simulating dissipative dynamics in fermionic systems is computationally challenging.
• Existing methods may lack accuracy or efficiency for complex systems.

Purpose of the Study:

• To present a novel numerical implementation of the stochastic equation of motion (SEOM) method.
• To introduce a minimal auxiliary space (MAS) mapping scheme for direct stochastic calculations.
• To provide an accurate and efficient computational tool for fermionic open quantum systems.

Main Methods:

• Development and implementation of the Minimal Auxiliary Space-Stochastic Equation of Motion (MAS-SEOM) method.
• Representation of time-dependent Grassmann fields using c-number noises and pseudo-operators.
• Analytic derivation of particle current and construction of system/pseudo-operators.

Main Results:

• The MAS-SEOM method is successfully applied to quantum impurity systems (Anderson impurity model).
• Numerical results for relaxation and voltage-driven dynamics are obtained.
• MAS-SEOM results are benchmarked against the highly accurate hierarchical equations of motion (HEOM) method, showing good agreement.

Conclusions:

• The MAS-SEOM approach offers a viable and accurate method for simulating dissipative dynamics in fermionic open quantum systems.
• The study discusses the advantages and limitations of the MAS-SEOM method.
• This work provides a valuable computational tool for researchers in quantum dynamics and transport.