Ground state instability in systems of strongly interacting fermions

TL;DR

This paper investigates the stability of strongly interacting fermion systems with repulsive interactions, revealing that their ground state restructuring involves topological transitions rather than Fermi condensation, with a phase diagram illustrating two types of such transitions.

Contribution

It demonstrates that in systems with screened Coulomb interactions, ground state restructuring occurs via topological transitions, not Fermi condensation, and constructs a phase diagram for these transitions.

Findings

Restructuring cannot be of Fermi condensation type for screened Coulomb interactions.

Identifies two types of topological transitions: Lifshitz-like and uniform strongly interacting system.

Phase diagram maps the relationship between screening parameter and coupling constant.

Abstract

We analyze stability of a fermion system with model repulsive pair interaction potential. The possibility for different types of restructuring of the Fermi ground state (at sufficiently great coupling constant) is related to the analytic properties of such potential. In particular, for the screened Coulomb law it is shown that the restructuring cannot be of the Fermi condensation type, known earlier for some exactly solvable models, and instead it belongs to the class of topological transitions (TT). For this model, a phase diagram has been built in the variables "screening parameter - coupling constant" which displays two kinds of TT: a 5/2-kind similar to the known Lifshitz transitions in metals, and a 2-kind characteristic for a uniform strongly interacting system.