Single-particle potential from resummed ladder diagrams

Abstract

A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by calculating the complex single-particle potential $U(p,k_f)+iW(p,k_f)$ 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 $a^2$. The limit $a\to \infty$ is studied as a special case and a strong momentum dependence of the real (and imaginary) single-particle potential is found. This indicates an instability against a phase transition to a state with an empty shell inside the Fermi sphere such that the density gets reduced by about 5%. For comparison, the same analysis is performed for the resummed particle-particle ladder diagrams alone. In this truncation an instability for hole-excitations near the Fermi surface is found at strong coupling. For the set of particle-hole ring diagrams the single-particle potential is calculated as well. Furthermore, the resummation of in-medium ladder diagrams to all orders is studied for a two-dimensional Fermi gas with a short-range two-body contact-interaction.

28 pages, 19 figures, to be published in European Physical Journal A

References in corpus (2)

• Microscopic optical potential from chiral nuclear forces
• Different scenarios of topological phase transitions in homogeneous neutron matter

Cited by in corpus (7)

• Phase structure of spin-imbalanced unitary Fermi gases
• Resurgence for superconductors
• Zero-temperature limit and statistical quasiparticles in many-body perturbation theory
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Toward precision Fermi liquid theory in two dimensions
• Particle-hole ring diagrams for fermions in two dimensions
• Local energy density functional for superfluid Fermi gases from effective field theory