Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions

A numerical method is presented for reproducing fermionic quantum gas microscope experiments in equilibrium. By employing nested componentwise direct sampling of fermion pseudodensity matrices, as they arise naturally in determinantal quantum Monte Carlo (QMC) simulations, a stream of pseudosnapshots 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 pseudosnapshot 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 one 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 pseudosnapshots after (signed) reweighting is identical to the distribution of snapshots from projective measurements.

Automated summary

The numerical method presented reproduces fermionic quantum gas microscope experiments in equilibrium by directly sampling pseudodensity matrices, resolving the sign problem in QMC simulations. It allows for the computation of distribution functions of arbitrary quantities defined in occupation number space and facilitates the computation of complicated conditional correlation functions.