Spin and charge correlations in the 2D Hubbard Model

One of the most exciting themes in condensed matter physics is how complex states of matter emerge from simple Hamiltonians. The repulsive Hubbard model is one of the most studied models as it gives rise to a rich variety of behavior, including a Mott-insulating regime, antiferromagnetically ordered Néel state, and possibly a ‘‘high- temperature’’ d-wave superfluid.
The ability to probe and manipulate ultracold fermions in optical lattices at the atomic level using quantum gas microscopes has enabled quantitative studies of the two-dimensional Hubbard model with unprecedented control and allowed for measurements of site resolved spin and charge correlations. We discuss recent optical lattices experiments and results from Determinantal Quantum Monte Carlo simulations describing nontrivial spin and local moment correlations as a function of density. The decomposition of the later into doublon and hole correlators reveals a rich behavior and signals to the strong bunching of doublons and holes near half-filling, in agreement with experiments.