Cite: A no-go theorem for purely local $(\rho,T)$ Dirac interpolation
Citation formats for prexiv:260513.aa1dp1. Use /cite.bib or /cite.ris for the raw files (TODO).
BibTeX
@misc{bai2026_260513aa1dp1,
title = {A no-go theorem for purely local $(\rho,T)$ Dirac interpolation},
author = {Dong Bai},
year = {2026},
note = {PreXiv id: prexiv:260513.aa1dp1},
doi = {10.99999/prexiv:260513.aa1dp1},
url = {https://prexiv.example/m/prexiv:260513.aa1dp1},
}
RIS
TY - GEN
TI - A no-go theorem for purely local $(\rho,T)$ Dirac interpolation
AU - Dong Bai
PY - 2026
DO - 10.99999/prexiv:260513.aa1dp1
ID - prexiv:260513.aa1dp1
UR - https://prexiv.example/m/prexiv:260513.aa1dp1
AB - We prove a sharp impossibility result for local Lieb--Oxford-type lower bounds on the indirect Coulomb energy of antisymmetric fermionic states. For a normalized \(N\)-fermion wavefunction \(\Psi\) write \(\rho_\Psi\) for its one-particle density, \(T_\Psi\) for its local kinetic energy density, and \(E_{\rm xc}(\Psi)\) for its indirect (exchange-correlation) energy. Let \(\mathcal R_\Psi\) be the dimensionless local kinetic ratio. Two constants control the discussion: the Dirac exchange constant \(C_D(q)=\tfrac{3}{4}(6/\pi)^{1/3}q^{-1/3}\) and the \emph{one-cell self-interaction constant} \(C_{\rm cell}=\tfrac{3}{5}(4\pi/3)^{1/3}\), which is strictly larger than \(C_D(q)\) for every spin multiplicity \(q\ge 1\). We show that any bounded function \(F\) with \(\limsup_{r\downarrow 0}F(r)<C_{\rm cell}\) cannot serve as the integrand of a universal pointwise lower bound \(E_{\rm xc}(\Psi)\ge -\!\int F(\mathcal R_\Psi)\rho_\Psi^{4/3}\) for arbitrarily large \(N\). The proof constructs antisymmetric many-cell states whose local data \((\rho_\Psi,T_\Psi)\) look like a flat Fermi sea but whose indirect energy is dominated by one-particle self-interaction. Consequently, no universal pointwise bound depending only on \((\rho_\Psi,T_\Psi)\) can have \(C_D(q)\) as its small-\(\mathcal R\) limit.
ER -
Plain text
Dong Bai (2026). A no-go theorem for purely local $(\rho,T)$ Dirac interpolation. PreXiv prexiv:260513.aa1dp1, doi:10.99999/prexiv:260513.aa1dp1.