2025/07/11 by Zhou‐Quan Wan, Shiwei Zhang, Wan, Zhou-Quan +1
Engineering · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Nuclear reactor physics and engineering #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2507.08937
openalex publication_date 2025/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
We revisit the infinite variance problem in fermionic Monte Carlo simulations, which is widely encountered in areas ranging from condensed matter to nuclear and high-energy physics. The different algorithms, which we broadly refer to as determinantal quantum Monte Carlo (DQMC), are applied in many situations and differ in details, but they share a foundation in field theory, and often involve fermion determinants whose symmetry properties make the algorithm sign-problem-free. We show that the infinite variance problem arises as the observables computed in DQMC tend to form heavy-tailed distributions. To remedy this issue retrospectively, we introduce a tail-aware error estimation method to correct the otherwise unreliable estimates of confidence intervals. Furthermore, we demonstrate how to perform DQMC calculations that eliminate the infinite variance problem for a broad class of observables. Our approach is an exact bridge link method, which involves a simple and efficient modification to the standard DQMC algorithm. The method introduces no systematic bias and is straightforward to implement with minimal computational overhead. Our results establish a practical and robust solution to the infinite variance problem, with broad implications for improving the reliability of a variety of fundamental fermion simulations.