Lieb's Theorem and Maximum Entropy Condensates

Coherent driving has established itself as a powerful tool for guiding many-body quantum system into desirable, coherent non-equilibrium state. A thermodynamically large will, however, almost always saturate to featureless infinite temperature state under continuous and so the optical manipulation of systems is considered feasible only if transient, prethermal regime exists, where heating suppressed. Here we show that, counterintuitively, in broad class lattices Floquet can actually be an advantageous effect. Specifically, prove that maximum entropy steady states which form upon ground Hubbard model on unbalanced bi-partite possess uniform off-diagonal long-range order remains finite even thermodynamic limit. This creation `hot' condensate occur \textit{any} driven lattice provides understanding how can, at macroscopic level, expose alter system. We discuss implications recent experiments observing emergent superconductivity photoexcited materials.