Origin of the Hubbard-model pseudogap at cuprate-like coupling strength
In plain words
At weak repulsion, computer studies trace the Hubbard model pseudogap to long-range magnetic fluctuations; whether the same holds at the strong repulsion relevant to cuprates is unsettled.
Precise statement
In the doped two-dimensional Hubbard model at $U/t \sim 6 \text{ to } 8$ and finite $T$, determine whether the antinodal pseudogap in the spectral function $A(k,\omega)$ arises from antiferromagnetic fluctuations with large correlation length $\xi(T)$ or from short-range singlet formation of Mott character, and locate the pseudogap endpoint in doping. An answer is a controlled calculation of $A(k,\omega)$ and $\xi(T)$ at strong coupling that discriminates the two.
What would settle it
Diagrammatic Monte Carlo or cluster calculations with controlled convergence at $U/t \sim 7$ showing whether the pseudogap opening tracks the growth of $\xi(T)$.
Status in the literature
Unverified note
Diagrammatic Monte Carlo (2024) established a spin-fluctuation pseudogap at weak to intermediate coupling; cluster methods at stronger coupling point to short-range Mott physics.