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Inchworm Monte Carlo Method for Open Quantum Systems
Author(s) -
Cai Zhenning,
Lu Jianfeng,
Yang Siyao
Publication year - 2020
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21888
Subject(s) - monte carlo method , resummation , quantum monte carlo , quantum , statistical physics , mathematics , work (physics) , diagrammatic reasoning , computer science , physics , mathematical analysis , quantum mechanics , logarithm , programming language , statistics
We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method—the inchworm Monte Carlo method—for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover, we introduce an integro‐differential equation formulation for open quantum systems, which illuminates the mathematical structure of the inchworm algorithm. This new formulation leads to an improvement of the inchworm algorithm by introducing classical deterministic time‐integration schemes. The numerical method is validated by applications to the spin‐boson model. © 2020 Wiley Periodicals, Inc.