Lieb's Theorem and Maximum Entropy Condensates

The maximum entropy steady states which form upon Floquet heating of the ground state of the Hubbard model on unbalanced bi-partite lattices are shown to possess uniform finite off-diagonal long-range order in the thermodynamic limit. For repulsive interactions the induced order corresponds to the formation of a spin-wave condensate, whilst for attractive interactions it instead corresponds to the formation of a superconducting, $\eta$-paired condensate. This creation of a `hot' condensate can occur on any periodically driven unbalanced lattice where the relevant SU(2) symmetry is preserved. Our results provide an understanding of how strong driving can expose order which has been suppressed by the lattice geometry - independent of any microscopic parameters. We discuss the implications of this for recent experiments observing emergent superconductivity in solid-state photoexcited compounds.