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Interacting fermions in two dimensions: beyond the perturbation theory

S. Gangadharaiah·D. L. Maslov·A. V. Chubukov·L. I. Glazman
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Abstract

We consider a system of 2D fermions with short-range interaction. A straightforward perturbation theory is shown to be ill-defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. We show that the divergences result from the interaction of fermions with the zero-sound collective mode. By re-summing the most divergent diagrams, we obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. We also show that the interaction with the zero sound does not affect a non-analytic, $T^{2}$-part of the specific heat.

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S. Gangadharaiah, D. L. Maslov, A. V. Chubukov, L. I. Glazman. 2005-01-03. Interacting fermions in two dimensions: beyond the perturbation theory. https://doi.org/10.1103/physrevlett.94.156407

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