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Physical review. B, Condensed matter

Fermi-liquid theory in the low-density two-dimensional Hubbard model

Sudhakar Yarlagadda, Susumu Kurihara

Published Oct 1, 1993• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.48.10567

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Physical review. B, Condensed matter•Jun 15, 1995•1 citation
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/\ensuremathϵ2{\mathrm{\ensuremath{\epsilon}}}^{2}\ensuremathϵ2ln\ensuremath{\epsilon}. Hence, we conclude that Fermi-liquid theory holds in our model.
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We study the Landau f function for a two-dimensional repulsive Fermi system in the dilute limit. We find the leading terms in the low-density expansion using second-order perturbation theory, following a method of Abrikosov and Khalatnikov. Further, using diagrammatic methods, we determine the essentially singular contribution coming from the two-hole bound state. The absence of a divergence in the f function, together with our earlier results on the quasiparticle lifetime, clearly demonstrates that the system is a Fermi liquid in the low-density regime.
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