Projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles

Area of Science:

• Computational Physics
• Quantum Field Theory
• Cold Atom Experiments

Background:

• Complex Langevin (CL) methods are used for numerical sampling in quantum field theory.
• Existing methods face challenges with sign problems and numerical stability for constrained systems.
• Cold atom experiments realize complex quantum systems like interacting Bose gases.

Purpose of the Study:

• To introduce a novel projected complex Langevin (CL) numerical sampling method.
• To address the sign problem and improve sampling of constrained stationary distributions with oscillatory character.
• To adapt and validate the method for quantum field theories in cold-atom experiments.

Main Methods:

• Developed a fictitious Langevin dynamics scheme with numerical projection.
• Incorporated complex-valued Lagrange multipliers for precise constraint enforcement.
• Applied the projected CL method to canonical and microcanonical ensembles of coherent state quantum field theories.

Main Results:

• The projected CL method successfully samples constrained stationary distributions.
• Demonstrated efficacy in simulating interacting Bose gases in cold-atom experiments.
• Achieved improved numerical stability and accuracy compared to previous state-of-the-art methods, even with larger time steps.

Conclusions:

• The projected CL method is a robust extension of real-valued Langevin processes for complex systems.
• This technique offers enhanced precision and stability for simulating quantum field theories with constraints.
• The method provides a powerful tool for analyzing thermodynamic observables in systems like cold Bose gases.