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

Arif Ullah; Lu Han; Yun-An Yan; Xiao Zheng; YiJing Yan; Vladimir Chernyak

doi:10.1063/1.5142166

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

J Chem Phys. 2020 May 29;152(20):204106. doi: 10.1063/1.5142166.

Authors

Arif Ullah¹, Lu Han¹, Yun-An Yan², Xiao Zheng¹, YiJing Yan³, Vladimir Chernyak¹

Affiliations

¹ Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
² School of Physics and Optoelectronic Engineering, Ludong University, Shandong 264025, China.
³ Hefei National Laboratory for Physical Sciences at the Microscale and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China.

PMID: 32486671
DOI: 10.1063/1.5142166

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-number 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 MAS-SEOM 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 method. The advantages and limitations of the present MAS-SEOM approach are discussed extensively.