Do spin-charge stripes appear in an isotropic two-dimensional Hubbard simulator?
In plain words
In some cuprates the holes line up in rows separated by magnetic stripes. Atom experiments saw stripes form in a simplified version of the model where holes move only along one direction; the full two-dimensional case has not shown them.
Precise statement
Square-lattice Fermi-Hubbard model with isotropic hopping, $U/t = 8 \text{ to } 10$, $\delta = 1/8$, $t'/t = 0 \text{ and } -0.2$, imaged by quantum gas microscopy. Measure spin-spin and hole-hole correlation functions and determine whether unidirectional stripe correlations with wavelength set by the doping appear at the lowest accessible $T/t$ (about 0.05 to 0.1). Answer: stripe correlation length versus $T/t$ and t', compared with finite-temperature numerics.
What would settle it
Microscope snapshots of a doped isotropic 2D lattice showing stripe correlations over several periods, matched to numerics at the measured temperature.
Status in the literature
Unverified note
Individual stripes were observed in a mixed-dimensional Fermi-Hubbard system in which holes hop only along one axis (Bourgund et al., Nature 2025, doi:10.1038/s41586-024-08270-7); no isotropic 2D observation was found in a 2026 arXiv search.