Inchworm Monte Carlo for exact non-adiabatic dynamics. I. Theory and algorithms

Area of Science:

• Quantum dynamics
• Computational physics
• Chemical physics

Background:

• Accurate simulation of real-time non-adiabatic dynamics is crucial in quantum mechanics.
• The dynamical sign problem poses a significant challenge for exact quantum simulations.
• Existing methods often struggle with computational scaling for complex systems.

Purpose of the Study:

• To present the inchworm Monte Carlo formalism for exact real-time non-adiabatic dynamics.
• To detail methods for suppressing the dynamical sign problem.
• To introduce a cumulant version of the inchworm Monte Carlo method with improved scaling.

Main Methods:

• Development of the inchworm Monte Carlo formalism.
• Formulation of the inchworm expansion with respect to system-bath coupling.
• Formulation of the inchworm expansion with respect to diabatic coupling.
• Introduction of a cumulant version of the inchworm Monte Carlo method.

Main Results:

• The inchworm Monte Carlo method effectively suppresses the dynamical sign problem.
• Two distinct formulations of the inchworm expansion are presented.
• The cumulant version demonstrates improved computational scaling.

Conclusions:

• The inchworm Monte Carlo method provides an exact approach to real-time non-adiabatic dynamics.
• The cumulant version offers a more efficient computational strategy.
• This methodology lays the groundwork for advanced quantum dynamics simulations.