Inchworm Monte Carlo for exact non-adiabatic dynamics. I. Theory and algorithms.
In this paper, we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. The latter approach motivates the development of a cumulant version of the inchworm Monte Carlo method, which has the benefit of improved scaling. This paper deals completely with methodology, while Paper II provides a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each.
Department of Chemistry, Columbia University, New York, New York 10027, USA.
Hsing-Ta
0000000266191861
HT
Chen
The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel.
Guy
0000000174044055
G
Cohen
Department of Chemistry, Columbia University, New York, New York 10027, USA.
David R
DR
Reichman