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Acta Physica Sinica

THEORY OF TWO-DIMENSIONAL FERMI LIQUIDS (Ⅰ)

Shi-Min Cui, CAI JIAN-HUA, (1)上海交通大学凝聚态物理研究所,上海,200030; (2)中国高等科学技术中心(世界实验室)理论物理分中心

Published Jan 1, 1990• 1 citation
Publisher

Abstract

It is shown that Landau's mean field theory of Fermi liquids is valid in two-dimensional case through evaluation of the quasiparticle life-time of a 2-D interacting Fermi systems at low density as well as the spin fluctuation of 2-D itinerant Fermi systems.
DOI
10.7498/aps.39.565

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We examine the validity of Fermi-liquid theory in the low-density two-dimensional Hubbard model. From the ground-state energy we obtain the quasiparticle energy and the Landau interaction function. Then we prove that the quasiparticle-interaction function is finite and that the quasiparticle residue is nonzero for repulsive interactions. We also find, as a function of the excitation energy \ensuremath{\epsilon}, that the quasiparticle lifetime \ensuremath{\sim}1/${\mathrm{\ensuremath{\epsilon}}}^{2}$ln\ensuremath{\epsilon}. Hence, we conclude that Fermi-liquid theory holds in our model.
Landau (1958) gave a rigorous microscopic derivation of his phenomenological Fermi -liquid theory starting from the first principles Hamiltonian of strongly interacting Fermions. The derivation is based on an asymptotic expansion in small parameters such as q/kF, bc.>/EF, kT/EF, where q and c.> represent the wave numbers and frequencies of real excitations of the system. Landau showed that the dynamics of these low-lying excitations (quasiparticles and collective modes) is governed by classical transport equations with all quantum many-body effects absorbed into effective interaction parameters. Landau's approach has been generalized to superfluid Fermi liquids and superconductors by Leggett (1965) and, going beyond linear response, by Eliashberg (1971). Their ideas merged into a recent review on the quasiclassical approach to superfluid 3 He by Serene and Rainer (1983). I will use the notation of this review throughout this paper. Landau's transport theory together with its offsprings will be called 'quasiclassical theory in the following. In this context it is important to mention that Eilenberger (1968) and Larkin and Ovchinnikov (1968) have shown that the complete theory of superconductors can be formulated as a quasiclassical transport theory. Surprisingly, this theory permits calculating microscopic properties, e.g. the quasiparticle excitation spectrum, which are predominantly governed by quantum effects.
Landau-Fermi liquid theory is conventionally believed to hold whenever the interacting single-particle density of states develops a $\ensuremath{\delta}$-like component at the Fermi surface, which is associated with quasiparticles. Here we show that a microscopic justification can be actually achieved under more general circumstances, even in the case where coherent quasiparticles are totally missing and the interacting single-particle density of states vanishes at the chemical potential as a consequence of a pole singularity in the self-energy.
It is shown that Landau’s quasiparticle formalism continues to work in systems with a fermion condensate. In the case of a finite system this formalism is suitable for describing the restructuring of states at the Fermi surface. It also works in an infinite system, and the idea of quasiparticles at low temperature as well-defined excitations at the Fermi surface remains valid. The quasiparticle lifetime is directly proportional to the temperature, and the density of states is inversely proportional to the temperature.