Spin degrees of freedom and flattening of the spectra of single-particle excitations in strongly correlated Fermi systems

The impact of long-range spin-spin correlations on the structure of a flat portion in single-particle spectra $\xi(p)$, which emerges beyond the point, where the Landau state loses its stability, is studied. We supplement the well-known Nozieres model of a Fermi system with limited scalar long-range forces by a similar long-range spin-dependent term and calculate the spectra versus its strength $g$. It is found that Nozieres results hold as long as $g>0$. However, with $g$ changing its sign, the spontaneous magnetization is shown to arise at any nonzero $g$. The increase of the strength $|g|$ is demonstrated to result in shrinkage of the domain in momentum space, occupied by the flat portion of $\xi(p)$, and, eventually, in its vanishing.Comment: 7 pages, 15 figure

Damping effects and the metal-insulator transition in the two-dimensional electron gas

The damping of single-particle degrees of freedom in strongly correlated two-dimensional Fermi systems is analyzed. Suppression of the scattering amplitude due to the damping effects is shown to play a key role in preserving the validity of the Landau-Migdal quasiparticle picture in a region of a phase transition, associated with the divergence of the quasiparticle effective mass. The results of the analysis are applied to elucidate the behavior of the conductivity $\sigma(T)$ of the two-dimensional dilute electron gas in the density region where it undergoes a metal-insulator transition.Comment: 7 pages, 6 figures. Improved and slightly extended version: new paragraph about Hall effect + new Fig.

Two Scenarios of the Quantum Critical Point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state, related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different {\it topological} scenario of the QCP, associated with the emergence of bifurcation points in equation $\epsilon(p)=\mu$ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction.Comment: 6 pages, added new discussion and 2 figure

Mechanisms driving alteration of the Landau state in the vicinity of a second-order phase transition

The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation $\epsilon(p)=\mu$, a condition that ordinarily has the Fermi momentum $p_F$ as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative alteration of the Landau state, well before the collapse of the collective degree of freedom that is responsible for the second-order transition. The competition between mechanisms that drive rearrangement of the Landau quasiparticle distribution is explored, taking into account the feedback of the rearrangement on the spectrum of critical fluctuations. It is demonstrated that the transformation of the Landau state to a new ground state may be viewed as a first-order phase transition.Comment: 16 pages, 10 figure

Rearrangement of the Fermi Surface of Dense Neutron Matter and Direct Urca Cooling of Neutron Stars

It is proposed that a rearrangement of single-particle degrees of freedom may occur in a portion of the quantum fluid interior of a neutron star. Such a rearrangement is associated with the pronounced softening of the spin-isospin collective mode which, under increasing density, leads to pion condensation. Arguments and estimates based on fundamental relations of many-body theory show that one realization of this phenomenon could produce very rapid cooling of the star via a direct nucelon Urca process displaying a $T^5$ dependence on temperature.Comment: 8 pages, 2 figure