Do two-body losses create long-range magnetic correlations in Hubbard lattices?
In plain words
Removing pairs of atoms that occupy the same lattice site leaves the survivors in special spin arrangements. Small double-well experiments saw the magnetic correlations flip sign, and whether this grows into extended magnetic order in a full lattice is open.
Precise statement
Two-component fermions in a 2D optical lattice described by the Hubbard model $(t, U)$ plus engineered on-site two-body loss at rate $\gamma$ (for example by photoassociation). Starting from an antiferromagnetically correlated state, determine the time evolution of the spin correlation function $C(r)$ of the surviving atoms, whether nearest-neighbour correlations reverse sign as predicted for double wells, and whether the reversed correlations extend beyond one lattice spacing, as functions of $\gamma/t$ and $U/t$. Answer: $C(r, \mathrm{time})$ measured and reproduced by Lindblad numerics.
What would settle it
Quantum gas microscope measurements of C(r) in a lossy 2D lattice compared with full Lindblad simulation.
Status in the literature
Sign reversal of the magnetic correlation was observed in isolated double wells (Honda et al., PRL 130, 063001, 2023); extended lattices are untested.