Heating-Induced Long-Range η Pairing in the Hubbard Model

We show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady states with long-range correlations between eta pairs. We induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal eta correlations. These correlations were first recognized in the superconducting eigenstates described in Yang's seminal Letter [Phys. Rev. Lett. 63, 2144 (1989)], which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism.