Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model including a Zeeman field*

Motivated by the ability to cool and bosonic and fermionic atoms down to ultra cold temperatures in optical lattices and experimental advances in site-resolved imaging, we study spatially resolved charge and spin correlations in the two-dimensional Fermi-Hubbard model using quantum Monte Carlo simulations. We investigate the behavior with and without a Zeeman field at a wide range of temperatures, including temperatures below currently reachable in experiments. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon reducing the filling or equivalently upon adding holes. At small filling, nearest-neighbor correlations between singly charged sites are negative, revealing the formation of a correlation hole, the suppressed probability of finding two fermions near each other. In the presence of a Zeeman field or equivalently in a spin-imbalanced atomic gas, we observe short-range canted antiferromagnetism at half-filling with stronger spin correlations in the direction orthogonal to the magnetization.

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