Stable non-Fermi liquid fixed point at the onset of incommensurate $2k_F$ charge density wave order

Abstract

We consider the emergence of a non-Fermi liquid fixed point in a two-dimensional metal, at the onset of a quantum phase transition from a Fermi liquid state to an incommensurate charge density wave (CDW) ordered phase. The momentum of the CDW boson is centred at the wavevector $\mathcal{Q}$, which connects a single pair of antipodal points on the Fermi surface with antiparallel tangent vectors. We employ the dimensional regularization technique in which the co-dimension of the Fermi surface is extended to a generic value, while keeping the dimension of the Fermi surface itself fixed at one. Although the system is strongly coupled at dimension $d=2$, the interactions become marginal at the upper critical dimension $d=d_c$, whose value is found to be $5/2$. Using a controlled perturbative expansion in the parameter $\epsilon =d_c-d$, we compute the critical exponents of the stable infrared fixed point characterizing the quantum critical point. The scalings of the original theory are determined by setting $\epsilon =1/2$, where the fermion self-energy is seen to scale with the frequency with a fractional power law of $2/3$, which is the telltale signature of a typical non-Fermi liquid phase.

In the published version, a singularity relevant for the UV was erroneously considered in the RG flow equations in the IR. This arxiv version includes the corrected results, showing that the number of coupling constant(s) is one (rather than two). The corrigendum has been published as Nucl. Phys. B 1018, 117047 (2025)

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Cited by in corpus (3)

• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Induction of non-Fermi liquids by critical cavity photons at the onset of superradiance
• Non-Fermi liquid behaviour of CDW instabilities in fractionally-filled moiré flatbands