Seven exact theorems for the Hubbard model on bipartite lattices d>1 are established from the [SU(2)×SU(2)×U(1)]/Z₂² symmetry.
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A two-channel Allen-Dynes framework delivers blind Tc predictions with R²=0.96 for 19 materials over 0.4-250 K using phonon and spin-fluctuation channels extracted from data, while showing that the Peotta-Torma geometric superfluid weight correlates with topology rather than pairing strength.
In the X-Q model the Néel-VBS transition is strongly first-order for N>2 because the X term cannot generate enough U(1) fluctuations of the dimer pattern.
One fixed parameter set in the layered t-J-V model accounts for acousticlike plasmon dispersions across the entire cuprate phase diagram in available RIXS data.
In the 2D Hubbard model, d-wave pairing is confined to superexchange frequencies with pair-forming processes at low frequencies and pair-breaking at higher ones, independent of the Hubbard U scale.
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Two-Channel Allen-Dynes Framework for Superconducting Critical Temperatures: Blind Predictions Across Five Orders of Magnitude and a Quantum-Metric No-Go Result
A two-channel Allen-Dynes framework delivers blind Tc predictions with R²=0.96 for 19 materials over 0.4-250 K using phonon and spin-fluctuation channels extracted from data, while showing that the Peotta-Torma geometric superfluid weight correlates with topology rather than pairing strength.