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Title: Entropy reduction needed to see d-wave correlations in Hubbard simulators
Plain: 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: 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 $s_{\mathrm{exp}}/s*$.
Settled by: 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.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status 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.
Posed since: (empty)