Recent Developments in Non-Fermi Liquid Theory

Abstract

Non-Fermi liquids arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticle, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the number of co-dimensions of Fermi surface. The second is a non-perturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.

23 pages; comments are welcome

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• A controlled expansion for certain non-Fermi liquid metals
• Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point
• Anisotropic Non-Fermi Liquids
• Emergence of a control parameter for the antiferromagnetic quantum critical metal
• Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals
• Two-point function of a $d=2$ quantum critical metal in the limit $k_F\to \infty$, $N_f\to 0$ with $N_f{k}_F$ fixed

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