Fermions under strong repulsion: from multiconnected Fermi surfaces to Fermi condensation

TL;DR

This paper explores how strong repulsive interactions in fermionic systems lead to complex multiconnected Fermi surfaces and Fermi condensation, revealing a transition from Fermi liquid to non-Fermi-liquid behavior at finite temperatures.

Contribution

It introduces a model showing the transition from a Fermi sphere to multiconnected Fermi surfaces and their evolution towards Fermi condensation at large N.

Findings

Transition occurs at g > g_cr, changing the ground state to multiconnected Fermi surfaces.

At large N, states tend toward Fermi condensate behavior.

Finite temperature crossover from Fermi liquid to non-Fermi-liquid behavior.

Abstract

We consider a system of fermions with mass m and model repulsive interaction U(q) = g/\sqrt{q^2 + q_0^2}, where q is the momentum transfer, q_0 the screening constant, and g > 0 the coupling constant. It is shown that at g > g_cr > 3\pi^2/m the system ground state is changed from fully occupied Fermi sphere to multiconnected Fermi sphere (MFS), consisting in N fully occupied spherical layers (icebergs) separated by empty spacers. An effective description is developed for such states at N >> 1, showing their tendency at N \to \infty to the Fermi condensate (FC) state known for the model U(q) = g/q [Khodel, Shaginyan, JETP Lett., 51, 553, 1990]. At finite temperatures, a crossover is predicted from the Fermi liquid behavior of MFS with effective mass m^* \sim m N/ln(N) to non-Fermi-liquid behavior with m^* \propto 1/T at T > T^* \sim T_F ln(N)/N.