Spin correlations in the bilayer Hubbard model with perpendicular electric field

We present a nonequilibrium steady-state implementation of the two-particle self-consistent method. This approach respects the Mermin-Wagner theorem and incorporates non-local spatial fluctuations through self-consistent static vertices. The real-frequency implementation allows to compute spectral properties without analytical continuation in both equilibrium and nonequilibrium. As an interesting application, we investigate spin correlations in the bilayer square lattice Hubbard model under a perpendicular static electric field. In equilibrium, the result yields spin correlations which are in good agreement with recent optical lattice experiments. Under a large enough static electric field, the inter-layer spin correlations switch from antiferromagnetic to ferromagnetic. We clarify how this phenomenon is linked to the nonequilibrium modifications of the spin excitation spectrum.