Single-particle potential from resummed ladder diagrams

Understand

A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by calculating the complex single-particle potential $U(p,k_f)+ i\,W(p,k_f)$ for momenta $p<k_f$ as well as $p>k_f$.

• The on-shell single-particle potential is constructed by means of a complex-valued in-medium loop that includes corrections from a test-particle of momentum $\vec p$ added to the filled Fermi sea.
• The single-particle potential $U(k_f,k_f)$ at the Fermi surface as obtained from the resummation of the combined particle and hole ladder diagrams is shown to satisfy the Hugenholtz-Van-Hove theorem.
• The perturbative contributions at various orders $a^n$ in the scattering length are deduced and checked against the known analytical results at order $a^1$ and $a^2$.