Does cold-atom Hubbard resistivity stay linear in temperature at low T?
In plain words
Many cuprates show electrical resistance growing in proportion to temperature, unlike ordinary metals. Atom experiments saw this down to moderate temperatures, and it is unknown whether it continues when the atoms are colder.
Precise statement
In the doped 2D Hubbard model at $U/t = 8$, $\delta = 0.1 \text{ to } 0.2$, measure the resistivity $\rho(T)$ from charge-current relaxation or from density diffusion via the Nernst-Einstein relation for $T/t$ from 1 down to 0.1. Answer: whether $\rho \sim T$ persists below $T = 0.3 t$ and whether the transport rate approaches the Planckian value $\hbar/\tau \sim k_B T$.
What would settle it
Transport measurements at T/t below 0.3 with independent thermometry, compared with finite-temperature numerics.
Status in the literature
Brown et al. (Science 2019) found $T$-linear resistivity above the Mott-Ioffe-Regel limit (the resistivity at which the mean free path equals one lattice spacing) at $U/t = 7.4$, $n = 0.82$, for $T/t$ from about 0.3 to 8; no data exist below about $0.3\,t$.