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We present a nonequilibrium steady-state implementation of the two-particleself-consistent method. This approach respects the Mermin-Wagner theorem andincorporates non-local spatial fluctuations through self-consistent staticvertices. The real-frequency implementation allows to compute spectralproperties without analytical continuation in both equilibrium andnonequilibrium. As an interesting application, we investigate spin correlationsin the bilayer square lattice Hubbard model under a perpendicular staticelectric field. In equilibrium, the result yields spin correlations which arein good agreement with recent optical lattice experiments. Under a large enoughstatic electric field, the inter-layer spin correlations switch fromantiferromagnetic to ferromagnetic. We clarify how this phenomenon is linked tothe nonequilibrium modifications of the spin excitation spectrum.

Spin correlations in the bilayer Hubbard model with perpendicular electric field