Lieb's Theorem and Maximum Entropy Condensates

TL;DR

This paper demonstrates that in certain driven lattice systems, heating can induce a stable, long-range ordered condensate state, challenging the usual view that heating destroys order in many-body quantum systems.

Contribution

It proves that maximum entropy steady states in driven Hubbard models on unbalanced lattices can host persistent off-diagonal long-range order, revealing heating as a constructive mechanism.

Findings

Steady states with off-diagonal long-range order exist under continuous driving.

Heating can create a 'hot' condensate in unbalanced lattices.

Implications for emergent superconductivity in photoexcited materials.

Abstract

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.