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

Hsing-Ta Chen1, Guy Cohen2, David R Reichman1

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This study introduces the inchworm Monte Carlo method for accurate real-time non-adiabatic dynamics, significantly reducing the dynamical sign problem by recycling information. A cumulant version offers improved computational scaling for complex quantum systems.

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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.