Ultraviolet-Infrared Mixing in Marginal Fermi Liquids

TL;DR

This paper explores how higher-loop quantum processes cause UV-IR mixing in marginal Fermi liquids, potentially destabilizing their weakly coupled fixed points and challenging existing theoretical descriptions.

Contribution

It reveals that UV-IR mixing due to gapless virtual Cooper pairs can significantly alter the low-energy behavior of marginal Fermi liquids, indicating a breakdown of the conventional patch description.

Findings

UV-IR mixing enhances low-energy coupling

Weakly coupled fixed point becomes measure-zero in low-energy limit

Patch description may not be valid for MFLs with long-range interactions

Abstract

When Fermi surfaces (FSs) 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 Letter, we point out a possibility in which higher-loop processes qualitatively change the picture through UV-IR mixing, in which the size of the 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 $(2+1)$-dimensional 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 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.