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 noncanonical Fermions and TomonagaLuttinger models. Generalizations are given for singletpaired superconductors, where one of the sumrules requires a testable assumption of particlehole 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 pseudoFermi surface, accessible to angle resolved photoemission, is defined using the zero crossings of the first frequency moment of a weighted spectral function.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 DOI:
 10.48550/arXiv.1808.00405
 arXiv:
 arXiv:1808.00405
 Bibcode:
 2018arXiv180800405S
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Superconductivity;
 Mathematical Physics
 EPrint:
 Total 29 pages