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arXiv:2208.01183

Exact Low-Energy Solution for Critical Fermi Surfaces

Tomer Ravid, Tom Banks

Published Aug 2, 2022• 1 citation
arXivHTMLPDF

Abstract

We derive multidimensional bosonization directly from the electron gas in a low-energy, low momentum regime where $ω\gg \frac{k^2}{k_F}$, such that the dispersion can be linearized. To reach this limit, the Fermi momentum and the number of patches are scaled simultaneously keeping the width of each patch finite. We apply this to obtain an exact low-energy solution of the problem of a Fermi surface coupled to a gapless boson, free of disorder and electron-electron scattering. Contrary to claims in the literature, we show that the bosonized theory exactly reproduces the $ω^{2/3}$ of electrons, previously obtained in large-$N$ theories. We argue that correction to the self-energy due to tangential dispersion are subdominant at sufficiently low energies such that $v_F k\gg \left(\frac{g^4 v_F}{k_F}\right)^{1/3} ω^{2/3}$, where $g$ is the coupling constant.

DOI
10.48550/arxiv.2208.01183

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We bosonize the low energy excitations of Fermi liquids in any number of dimensions in the limit of long wavelengths. The bosons are a coherent superposition of electron-hole pairs and are related with the displacements of the Fermi surface in some arbitrary direction. A coherent-state path integral for the bosonized theory is derived and it is shown to represent histories of the shape of the Fermi surface. The Landau theory of Fermi liquids can be obtained from the formalism in the absence of nesting of the Fermi surface and singular interactions. We show that the Landau equation for sound waves is exact in the semiclassical approximation for the bosons.
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