Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation

TL;DR

This paper details the numerical implementation of the stochastic equation of motion method for fermionic open quantum systems, introducing a minimal auxiliary space mapping and benchmarking against established methods.

Contribution

It introduces a minimal auxiliary space scheme for stochastic calculations in fermionic systems and demonstrates its application to quantum impurity models.

Findings

Successfully applied MAS-SEOM to Anderson impurity model

Benchmark results show good agreement with HEOM

Discussed advantages and limitations of the method

Abstract

This paper provides a detailed account of the numerical implementation of the stochastic equation of motion (SEOM) method for the dissipative dynamics of fermionic open quantum systems. To enable direct stochastic calculations, a minimal auxiliary space (MAS) mapping scheme is adopted, with which the time-dependent Grassmann fields are represented by c-numbers noises and a set of pseudo-operators. We elaborate on the construction of the system operators and pseudo-operators involved in the MAS-SEOM, along with the analytic expression for the particle current. The MASSEOM is applied to study the relaxation and voltage-driven dynamics of quantum impurity systems described by the single-level Anderson impurity model, and the numerical results are benchmarked against those of the highly accurate hierarchical equations of motion (HEOM) method. The advantages and limitations of the present MAS-SEOM approach are discussed extensively.