Noise, sign problems, and statistics

TL;DR

The paper investigates how sign problems cause heavy-tailed distributions in many-body system simulations and introduces a new statistical method to accurately extract ground state energies, demonstrated with toy and lattice models.

Contribution

It proposes an alternative statistical approach to address sign problems in many-body simulations, improving energy extraction accuracy.

Findings

Heavy-tailed correlator distributions are linked to sign problems.

The new method effectively extracts ground state energies.

Validated with toy models and lattice data for unitary fermions.

Abstract

We show how sign problems in simulations of many-body systems can manifest themselves in the form of heavy-tailed correlator distributions, similar to what is seen in electron propagation through disordered media. We propose an alternative statistical approach for extracting ground state energies in such systems, illustrating the method with a toy model and with lattice data for unitary fermions.