Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions

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

5 + 10 pages, 3 + 8 figures, including link to program code, published version

References in corpus (4)

• A Quantum Gas Microscope for Fermionic Atoms
• Microscopic spinon-chargon theory of magnetic polarons in the t-J model
• Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model
• Full Counting Statistics for Interacting Fermions with Determinantal Quantum Monte Carlo Simulations

Cited by in corpus (5)

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• Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation
• Sampling Electronic Fock States using Determinant Quantum Monte Carlo
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice