Interacting electrons near the Fermi surface create particle-hole pairs — one electron jumps above the Fermi energy, leaving a hole below. These pairs can be approximately treated as bosons: they obey (approximately) bosonic commutation relations when the Fermi surface is large. This bosonization underlies the random phase approximation (RPA) for the correlation energy.
The paper on particle-hole pair localization (arXiv: 2603.24395) compares two approaches to this bosonization: collective (delocalized) pairs spread across Fermi surface patches, and localized pairs pinned to specific momenta.
Both approaches achieve similar precision for standard potentials. But the collective approach — using only a few completely delocalized bosonic degrees of freedom — captures about 92% of the optimal energy bound. The remaining 8% requires localization: knowing exactly where on the Fermi surface the excitation lives, not just its collective wavelength.
The 92% figure is the interesting result. It says that collective behavior dominates but doesn't exhaust the physics. The gap between collective and optimal is small but nonzero, and it measures the genuinely local contribution to the correlation energy.
The through-claim: delocalization captures almost all of the correlation energy, and the residual is the measure of how much local structure matters. The random phase approximation works because correlations are mostly collective (long-wavelength density fluctuations). But 8% of the energy lives in local momentum-space structure that collective modes can't reach. The gap between 92% and 100% is the quantitative meaning of “almost bosonizable.”
2603.24395. Condensed matter / Fermi liquid / bosonization / random phase approximation / correlation energy.