Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions

TL;DR

This paper introduces a numerical method that accurately reproduces quantum gas microscopy results for interacting lattice fermions by sampling from fermionic density matrices, enabling detailed analysis of occupation number distributions.

Contribution

The method uses nested componentwise sampling of fermion pseudo-density matrices within determinantal QMC, allowing exact reproduction of experimental occupation number distributions.

Findings

Weak sign problem in large parameter regimes

Enables computation of arbitrary occupation number distributions

Facilitates analysis of complex correlation functions

Abstract

A numerical method is presented for reproducing fermionic quantum gas microscope experiments in equilibrium. By employing nested componentwise direct sampling of fermion pseudo-density matrices, as they arise naturally in determinantal quantum Monte Carlo (QMC) simulations, a stream of pseudo-snapshots of occupation numbers on large systems can be produced. There is a sign problem even when the conventional determinantal QMC algorithm can be made sign-problem free, and every pseudo-snapshot comes with a sign and a reweighting factor. Nonetheless, this "sampling sign problem" turns out to be weak and manageable in a large, relevant parameter regime. The method allows to compute distribution functions of arbitrary quantities defined in occupation number space and, from a practical point of view, facilitates the computation of complicated conditional correlation functions. While the projective measurements in quantum gas microscope experiments achieve direct sampling of occupation number states from the density matrix, the presented numerical method requires a Markov chain as an intermediate step and thus achieves only indirect sampling, but the full distribution of pseudo-snapshots after (signed) reweighting is identical to the distribution of snapshots from projective measurements