Entropy reduction needed to see d-wave correlations in Hubbard simulators
In plain words
Cooling atoms in a lattice is limited by how much disorder (entropy) remains per site. The question is how far below today's best entropy an experiment must go before pairing becomes visible.
Precise statement
Let $s_{\mathrm{exp}}$ be the entropy per site (units of $k_B$) reached in current doped quantum-gas-microscope samples. For the 2D Hubbard model at $U/t = 8$, $\delta = 0.125$, $t'/t = -0.2$, determine the entropy per site $s*$ below which the d-wave pair correlation length exceeds 10 lattice sites, and hence the required reduction $s_{\mathrm{exp}} - s*$. Answer: $s*$ with error bars from controlled finite-temperature numerics and the ratio $s_{\mathrm{exp}}/s*$.
What would settle it
Controlled finite-temperature numerics (for example diagrammatic Monte Carlo or tensor-network methods with error bars) giving the pair correlation length as a function of entropy per site at the stated parameters.
Status in the literature
Unverified note
Ground-state DMRG and auxiliary-field quantum Monte Carlo find d-wave order coexisting with partially filled stripes at $t' \ne 0$ (Xu et al., Science 2024); controlled finite-temperature values of $s*$ are lacking.