Monte Carlo sampling of complex actions in extended state spaces

Area of Science:

• Computational physics
• Quantum mechanics
• Statistical mechanics

Background:

• Complex actions arise in diverse physical systems, including quantum chromodynamics and nonequilibrium quantum evolution.
• The sign problem is a major hurdle in computations involving complex actions.
• Complex Langevin dynamics offers a broadly applicable computational approach but faces challenges with unphysical fixed points.

Purpose of the Study:

• To develop a robust computational framework for systems with complex actions.
• To address the issue of unphysical fixed points in complex Langevin dynamics.
• To establish a method for constructing reliable sampling schemes for complex actions.

Main Methods:

• A novel approach based on a Markov chain Monte Carlo scheme in an extended state space.
• Derivation of an explicit real sampling process for generalized complex Langevin dynamics.
• Utilizing detailed-balance equations to impose constraints for physical sampling.

Main Results:

• The proposed method ensures that the sampling process is physical under specific constraints.
• Complex Langevin dynamics is re-derived from a new theoretical perspective.
• A framework is established for constructing new, explicit sampling schemes for complex actions.

Conclusions:

• The developed Markov chain Monte Carlo approach provides a reliable method for complex action computations.
• This work offers a way to detect and avoid unphysical fixed points in complex Langevin dynamics.
• The established framework facilitates the development of advanced computational techniques for quantum systems.