Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model: Comparison between quantum Monte Carlo simulations and optical lattice emulators*

I will report on the current status and challenges faced by quantum Monte Carlo simulations to obtain quantitative information about the spatially resolved charge and spin correlations in the two-dimensional Fermi-Hubbard model. The computational results will be compared with those obtained in site-resolved imaging experiments with fermionic atoms in optical lattices. I will also discuss results with and without a Zeeman field at a wide range of temperatures, including temperatures below currently reachable in experiments. Some of the open questions I will discuss are: (1) Are there signatures of fractionalization of the fermionic spectral function? (2) How close are we to observing d-wave superconductivity in the simulations and experiments? (3) What is the sign problem and in which regions of parameter space is it most problematic?

[1] L. W. Cheuk, et. al., Science 353, 1260 (2016).
[2] P. T. Brown, et. al, Science 357, 1385 (2017).