Ultraviolet-Infrared Mixing in Marginal Fermi Liquids

Abstract

When Fermi surfaces (FS) are subject to long-range interactions that are marginal in the renormalization-group sense, Landau Fermi liquids are destroyed, but only barely. With the interaction further screened by particle-hole excitations through one-loop quantum corrections, it has been believed that these marginal Fermi liquids (MFLs) are described by weakly coupled field theories at low energies. In this paper, we point out a possibility in which higher-loop processes qualitatively change the picture through UV/IR mixing, in which the size of FS enters as a relevant scale. The UV/IR mixing effect enhances the coupling at low energies, such that the basin of attraction for the weakly coupled fixed point of a (2+1)-dimemsional MFL shrinks to a measure-zero set in the low-energy limit. This UV/IR mixing is caused by gapless virtual Cooper pairs that spread over the entire FS through the marginal long-range interactions. Our finding signals a possible breakdown of the patch description for the MFL, and questions the validity of using the MFL as the base theory in a controlled scheme for non-Fermi liquids that arise from relevant long-range interactions.

Gifts from anomalies: Exact results for Landau phase transitions in metals

“…The validity of this expansion was recently called into question in Ref. [31], who found log 2 divergences in a subset of three-loop diagrams due to large-momentum scattering in the = 0 marginal Fermi liquid base theory that causes virtual Cooper pairs to spread across the entire Fermi surface. Nevertheless, since this divergence appears only at third leading order in 1/N f , one can still hope to verify the prediction of the anomaly to leading order in 1/N f .…”

“…The simplest perturbative approach using a large-N expansion in the number of fermion species has been demonstrated to suffer from infrared (IR) issues, rendering it uncontrolled [29]. Other attempts at controlled perturbative deformations involve spatial non-locality [26,30,31], varying the co-dimension of the Fermi surface [32], introducing matrix bosons [28,33,34], and, most recently, adding random couplings between different species of bosons and fermions [35,36]. While each of these approaches may allow access to a formally controlled IR fixed point the connection of such a fixed point to the original problem is not always clear.…”