The Exact Dome
# The Exact Dome
The cuprate superconductors have resisted exact theoretical treatment for decades. Their phase diagram — the dome-shaped dependence of critical temperature on doping — emerges from the interplay of strong electron correlations and an unusual Fermi surface that includes arcs rather than closed contours. Numerical methods (quantum Monte Carlo, DMFT, tensor networks) produce dome-shaped Tc curves, but the computational complexity prevents systematic understanding of which features are universal and which are model-specific.
Zhou and colleagues (arXiv:2603.24977, March 2026) construct an exactly solvable model with Fermi arcs and strong correlations that reproduces the dome-shaped Tc profile analytically. The Fermi arcs — disconnected segments of the Fermi surface, characteristic of the cuprate normal state — suppress Tc through a many-body effect that goes beyond simple Fermi surface reduction. Naively, fewer Fermi surface states means a lower density of states at the Fermi level, which should reduce the pairing and lower Tc proportionally. The exact solution shows the suppression is stronger than this: the arcs create a correlation effect that further reduces the effective pairing interaction.
The gap-to-Tc ratio substantially exceeds the mean-field BCS prediction (2Δ/kTc ≈ 3.53 for weak coupling). The exact solution shows the deviation is intrinsic to the Fermi arc geometry, not an artifact of strong coupling or exotic pairing symmetry. The arcs distort the relationship between the gap magnitude and the critical temperature because the pairing is concentrated on the arc segments rather than distributed uniformly around a closed Fermi surface.
The structural observation: an exactly solvable model in strongly correlated superconductivity is not merely a pedagogical simplification. It provides analytical proof that specific features — the dome shape, the enhanced gap ratio, the many-body arc suppression — are consequences of Fermi arc geometry under strong correlation, independent of the specific microscopic Hamiltonian. The exactness separates the universal from the particular in a way that no numerical study can.
