Fermi surface volume of interacting systems

Abstract Three Fermion sumrules for interacting systems are derived at T = 0 , involving the number expectation N ( μ ) , canonical chemical potentials μ ( m ) , a logarithmic time derivative of the Greens function γ k → σ and the static Greens function. In essence we establish at zero temperature the sumrules linking: N ( μ ) ↔ ∑ m Θ ( μ − μ ( m ) ) ↔ ∑ k → , σ Θ γ k → σ ↔ ∑ k → , σ Θ G σ ( k → , 0 ) . Connecting them across leads to the Luttinger and Ward sumrule, originally proved perturbatively for Fermi liquids. Our sumrules are nonperturbative in character and valid in a considerably broader setting that additionally includes non-canonical Fermions and Tomonaga–Luttinger models. Generalizations are given for singlet-paired superconductors, where one of the sumrules requires a testable assumption of particle–hole symmetry at all couplings. The sumrules are found by requiring a continuous evolution from the Fermi gas, and by assuming a monotonic increase of μ ( m ) with particle number m . At finite T a pseudo-Fermi surface, accessible to angle resolved photoemission, is defined using the zero crossings of the first frequency moment of a weighted spectral function.