Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model

Optical lattice experiments with ultracold fermion atoms and quantum gas microscopy have recently realized direct measurements of magnetic correlations at the site-resolved level. We calculate the short-range spin correlation functions in the ground state of the two-dimensional repulsive Hubbard model with the auxiliary-field Quantum Monte Carlo (AFQMC) method. The results are numerically exact at half filling where the fermion sign problem is absent. Away from half-filling, we employ the constrained path AFQMC approach to eliminate the exponential computational scaling from the sign problem. The constraint employs unrestricted Hartree-Fock trial wave-functions with an effective interaction strength U , which is optimized self-consistently within AFQMC. Large supercells are studied, with twist averaged boundary conditions as needed, to reach the thermodynamic limit. We find that the nearest-neighbor spin correlation always increases with the interaction strength U , contrary to the finite-temperature behavior where a maximum is reached at a finite U value. We also observe a change of sign in the next nearest neighbor spin correlation with increasing density, which is a consequence of the buildup of the long-range anti-ferromagnetic correlation. We expect the results presented in this work to serve as a benchmark as lower temperatures are reached in ultracold atom experiments.