Lieb’s Theorem and Maximum Entropy Condensates

Joseph Tindall1, Frank Schlawin2,3, Michael Sentef2, and Dieter Jaksch1,3,4

1Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
2Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany
3The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, Hamburg, Germany
4Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany

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

In general, heat is deleterious towards quantum effects. Under certain symmetry constraints, however, this is not true and heating can be used to re-arrange and expose order in a quantum system.
In this article we show how, in a paradigmatic electronic system, the amount of order which results from this process can be directly related to certain geometrical properties of the underlying lattice. This allows us to identify a range of lattice structures where heating can be used to manipulate and manifest quantum order even at the macroscopic level.
We discuss possible experimental realisations of our work and its potential as a novel method for engineering and controlling superconductivity.

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