Fermi Surface Volume of Interacting Systems

Abstract

Three Fermion sumrules for interacting systems are derived at T=0, involving the number expectation $\bar{N}(\mu )$, canonical chemical potentials $\mu (m)$, a logarithmic time derivative of the Greens function ${\gamma }_{\vec{k}\sigma }$ and the static Greens function. In essence we establish at zero temperature the sumrules linking: $$\bar{N}(\mu )\leftrightarrow \sum _m\Theta (\mu -\mu (m))\leftrightarrow \sum _{\vec{k},\sigma }\Theta \left({\gamma }_{\vec{k}\sigma }\right)\leftrightarrow \sum _{\vec{k},\sigma }\Theta \left(G_{\sigma }(\vec{k},0)\right).$$ 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.

Total 29 pages ; Enlarged discussion from earlier version

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Cited by in corpus (1)

• Extremely Correlated Superconductors