# Heating-Induced Long-Range $\eta$-Pairing in the Hubbard Model

## TL;DR

This paper demonstrates that heating the spin degrees of freedom in the Hubbard model to infinite temperature can induce long-range $ ext{eta}$-pairing correlations in the steady state, independent of the heating method, due to symmetry properties.

## Contribution

It reveals how symmetry considerations enable long-range $ ext{eta}$-pairing in the Hubbard model's steady state under heating, extending the understanding of nonequilibrium states.

## Key findings

- Steady states exhibit distance-invariant $ ext{eta}$-correlations.
- Long-range $ ext{eta}$-pairing arises from symmetry, not microscopic details.
- Heating to infinite temperature melts spin order but induces $ ext{eta}$-pairing.

## Abstract

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. With 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 recognised in the superconducting eigenstates in Yang's seminal paper [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.