Mitigating spikes in fermion Monte Carlo methods by reshuffling measurements

TL;DR

This paper introduces a reshuffling method to reduce heavy-tailed distributions in fermion Monte Carlo simulations, significantly improving statistical efficiency especially for local observables.

Contribution

It presents a simple synchronization change that suppresses heavy tails in fermion Monte Carlo measurements, enhancing accuracy and speed for local observables.

Findings

Speedup of up to two orders of magnitude for local observables.

Moderate speedup (5-10 times) for spatial correlators.

Method effective regardless of auxiliary field type.

Abstract

We propose a method to mitigate heavy-tailed distributions in fermion Quantum Monte Carlo simulations originating from zeros of the fermion determinant. In this case the second moment of the observables might be not well defined, and we show that by merely changing the synchronization between local updates and computation of observables, one can reduce the prefactor of the heavy-tailed distribution, thus substantially suppressing statistical fluctuations of observables. We also show that the average, or the first moment, is well defined and hence is independent on our measuring scheme. The method is especially suitable for local observables similar to e.g. double occupancy, where the resulting speedup can reach two orders of magnitude. For observables, containing spatial correlators, the speedup is more moderate, but still ranges between five and ten. Our results are independent on the nature of the auxiliary field, discrete or continuous, and pave the way to improve measurement strategies for Hybrid Monte Carlo simulations.