Reducing autocorrelation time in determinant quantum Monte Carlo using the Wang-Landau algorithm: Application to the...

Area of Science:

• Computational Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• Monte Carlo calculations require simulation times significantly longer than autocorrelation times for reliable results.
• The Holstein model, a type of lattice fermion model, is known for exhibiting exceptionally long autocorrelation times, hindering efficient simulation.

Purpose of the Study:

• To develop and validate a novel computational method to address the challenge of long autocorrelation times in quantum Monte Carlo simulations.
• To improve the efficiency of simulating complex lattice fermion models, specifically the Holstein model.

Main Methods:

• Employed the Wang-Landau algorithm within the determinant quantum Monte Carlo framework.
• Implemented flat-histogram sampling in the "configuration weight space" to reduce autocorrelation time.
• Validated the proposed method on the Holstein model using both square and honeycomb lattices.

Main Results:

• The Wang-Landau algorithm significantly reduced autocorrelation time in determinant quantum Monte Carlo simulations.
• The method demonstrated effectiveness in the challenging Holstein model on different lattice structures.
• A trade-off between reduced autocorrelation time and some sampling efficiency was observed.

Conclusions:

• The Wang-Landau assisted determinant quantum Monte Carlo method offers a viable approach to simulate models with long autocorrelation times.
• This technique potentially expands the scope of quantum Monte Carlo simulations for complex physical systems.