Fermi surface volume of interacting systems

Three Fermion sumrules for interacting systems are derived at T = 0, involving the number expectation (N) over bar(mu), canonical chemical potentials mu(m), a logarithmic time derivative of the Greens function gamma((k) over right arrow sigma), and the static Greens function. In essence we establish at zero temperature the sumrules linking: (N) over bar(mu) <-> Sigma(m) Theta(mu-mu(m)) <-> Sigma((k) over right arrow.sigma) Theta (gamma((k) over right arrow sigma)) <-> Sigma((k) over right arrow sigma) Theta(G(sigma) ((k) over right arrow, 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 mu(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. (C) 2019 Elsevier Inc. All rights reserved.