A simple derivation of the zero-temperature BCS functional from the reduced BCS Hamiltonian
Year: 2026
Type: preprint
Abstract: We consider a grand-canonical reduced BCS Hamiltonian on the full fermionic Fock space with an attractive pairing interaction supported in an energy shell around the Fermi surface. For fixed chemical potential, we prove that the exact finite-volume ground-state energy differs from the minimum of the corresponding finite-volume BCS functional by a volume-independent error. As a consequence, the BCS variational principle is exact for the ground-state energy density in the thermodynamic limit.
Source: arXiv (Cornell University)
Authors: Hainzl, Christian, Panza, Riccardo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208778899