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arXiv · 2109.00004

Ultraviolet-Infrared Mixing in Marginal Fermi Liquids

Weicheng Ye·Sung-Sik Lee·Liujun Zou
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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.

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Weicheng Ye, Sung-Sik Lee, Liujun Zou. 2021-08-31. Ultraviolet-Infrared Mixing in Marginal Fermi Liquids. https://doi.org/10.1103/physrevlett.128.106402

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