Tomer Ravid | Searcharxiv

arXiv2024

Electrons Lost in Phase Space

I review the formalism of patch bosonization of Fermi surfaces, with a focus on the problem of a two-dimensional metal at a quantum critical point. I argue that this formalism is fundamentally inapplicable to the problem, except in synthetic limits. One such limit is the small-$N$ limit, which was already discussed in early studies of the problem; a similar but slightly less unphysical large-$N$ limit is proposed. I show that it is at least formally possible to construct perturbative expansions around these synthetic limits. However, I argue that nonperturbative effects become important when $N\sim1$.

cond-mat.str-el↗

arXiv2022

Exact Low-Energy Solution for Critical Fermi Surfaces

We derive multidimensional bosonization directly from the electron gas in a low-energy, low momentum regime where $\omega\gg \frac{k^2}{k_F}$, 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 $\omega^{2/3}$ 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 $v_F k\gg \left(\frac{g^4 v_F}{k_F}\right)^{1/3} \omega^{2/3}$, where $g$ is the coupling constant.

cond-mat.str-el↗