Mitigating spikes in fermion Monte Carlo methods by reshuffling measurements

Area of Science:

• Computational Physics
• Quantum Many-Body Systems

Background:

• Fermion quantum Monte Carlo (FQMC) simulations can suffer from heavy-tailed distributions due to zeros in the fermion determinant.
• These distributions can lead to ill-defined higher moments of observables, complicating accurate measurements.
• Existing methods may struggle with the computational cost associated with mitigating these fluctuations.

Purpose of the Study:

• To develop a novel method for mitigating heavy-tailed distributions in FQMC simulations.
• To demonstrate that the average (first moment) of observables remains well-defined regardless of the measurement scheme.
• To quantify the efficiency gains for different types of observables.

Main Methods:

• Modifying the synchronization between local updates and the computation of observables.
• Analyzing the impact of this synchronization change on the prefactor of heavy-tailed distributions.
• Applying the method to both local observables and those involving spatial correlators.

Main Results:

• The proposed method effectively reduces the prefactor of heavy-tailed distributions, significantly suppressing statistical fluctuations.
• The average of observables is shown to be robust and independent of the synchronization strategy.
• Speedups of up to two orders of magnitude were achieved for local observables like double occupancy.
• Moderate speedups (5-10x) were observed for observables including spatial correlators.

Conclusions:

• The synchronization adjustment offers a practical and efficient way to improve FQMC simulations.
• This technique is broadly applicable, independent of the auxiliary field's nature (discrete or continuous).
• The findings pave the way for enhanced measurement strategies in hybrid Monte Carlo simulations.