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arXiv:1212.3428 · Chinese Physics C

Rearrangements of interacting Fermi liquids

Rong-Yao Yang, Wei-Zhou Jiang

Published Oct 1, 2014• 0 citations
arXivHTMLPDF

Abstract

The stability condition of the Landau Fermi liquid theory may be broken when the interaction between particles is strong enough. In this case, the ground state is reconstructed to have a particle distribution different from the Fermi-step function. For specific instances, one case with the vector boson exchange and another with the relativistic heavy-ion collision are taken into consideration. With the vector boson exchange, we find that the relative weak interaction strength can lead to the ground-state rearrangement as long as the fermion mass is large enough. It is found that the relativistic heavy-ion collision may also cause the ground-state rearrangement, affecting the statistics of the collision system.

DOI
10.1088/1674-1137/38/10/104104

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The stability condition of the Landau Fermi liquid theory may be broken when the interaction between particles is strong enough. In this case, the ground state is reconstructed to have a particle distribution different from the Fermi-step function. For specific instances, one case with the vector boson exchange and another with the relativistic heavy-ion collision are taken into consideration. With the vector boson exchange, we find that the relative weak interaction strength can lead to the ground-state rearrangement as long as the fermion mass is large enough. It is found that the relativistic heavy-ion collision may also cause the ground-state rearrangement, affecting the statistics of the collision system.
The structure of the ground state beyond the instability point of the quasiparticle system with a Fermi-step momentum distribution is studied within the model of a Fermi liquid with a strong repulsive interaction. A ground-state rearrangement occurs as the interaction strength is increased beyond a certain critical value. Numerical investigation of the initial stage of this structural transition shows that there are two temperature regions, corresponding to different scenarios of the rearrangement. While for temperature T larger than some characteristic temperature the behaviour of the system is the same as that in the case of fermion condensation, for an intermediate structure with a multi-connected quasiparticle momentum distribution arises.
We examine the structure of the ground state of a homogeneous Fermi liquid beyond the instability point of the Fermi-like quasiparticle momentum distribution in the effective-functional method with a strong repulsive effective interaction. A numerical study of the initial stage of rearrangement of the ground state, based on a simple effective functional, showed that there exists a temperature T 0 , above which the behavior of the system is the same as in the theory of fermion condensation, and for T < T 0 the scenario of rearrangement of the ground state is different. At low temperatures an intermediate structure arises, with a multiply connected quasiparticle momentum distribution. The transition of this structure with growth of the coupling constant to a state with a fermion condensate is discussed.
The set of equations for the two-particle Green's functions in a nonequilibrium medium is derived in the diffusive approximation. Both the two- and single-particle Green's functions are calculated when matter is in the ground state. It is shown that the Landau Fermi-liquid consideration is correct when the interaction between particles in matter is rather weak or when matter is not too dense. In the opposite cases the energy spectrum of the particles is rearranged so that the step in the momentum distribution of the particles disappears. The applicability of the Landau Fermi-liquid theory is established in the general case.
Low-temperature properties of 3D interacting fermion systems are well described by Landau's theory of Fermi liquids; for reviews see, e.g. [183, 184]. It involves only excitations of the system around the Fermi surface on energy scales small compared to the Fermi energy. Excitations are well described by quasi-particles which are in one-to-one correspondence with the bare particles. The bare-particle interaction does not break the qualitative picture of non-interacting system, but renormalizes the dynamical characteristics (the effective mass and the pair interaction) of quasi-particles. Within the microscopic Green function formalism, the existence of quasi-particles is equivalent to assuming that the self-energy correction Σ( k , ω) is regular (has only short-range contributions in time and space) close to the Fermi surface. The lifetime of quasi-particles τ α(ε k −ε F ) −2 is long enough to consider them as well-defined eigenstates over long time-scales. The momentum occupation number of the bare particles exhibits a sharp discontinuity when crossing the Fermi momentum. The charge and spin degrees of freedom of quasi-particle always travel together. The Landau theory breaks down in 1D systems of interacting fermions which have a very specific Fermi surface consisting of two points ± k F . In such systems, the self-energy Σ( k , ω) no longer possesses the analytic properties required for introducing quasi-particles. In contrast to Fermi liquids, the momentum occupation number of the bare particles in the ground state is continuous at the Fermi momentum. Moreover, the charge and spin excitations are separated.
Following a suggestion of Khodel' and Shaginyan (KS), it is shown that a Hartree Fock description of Fermi liquids can lead to very strange results when the interaction has long range. For instance, the sharp drop of particle distribution at the Fermi level can be smeared over a finite kkk-range, with a flat plateau in the quasiparticle energy. In practice, such an effect appears as an artefact of the Hartree Fock approximation. The KS effect occurs only for an attraction, in which case it is hidden by superconductivity. Moreover, the enhanced quasiparticle collision rate makes the Hartree Fock approximation untenable. Finally, screening of a strong long range interaction is such that the instability threshold cannot be reached.