Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

UV/IR Mixing in Marginal Fermi Liquids

Weicheng Ye, Sung-Sik Lee, Liujun Zou

Published Sep 2, 2021• 7 citations
OpenAlex

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.

Related papers

Ultraviolet-Infrared Mixing in Marginal Fermi Liquids

Weicheng Ye, Sung-Sik Lee, Liujun Zou

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.

arXiv:2109.00004•Physical Review Letters•Mar 11, 2022•18 citations

Ultraviolet/infrared mixing in non-Fermi liquids

Ipsita Mandal, Sung-Sik Lee

We study low-energy effective-field theories for non-Fermi liquids with Fermi surfaces of general dimensions and codimensions. When the dimension of the Fermi surface is greater than one, low-energy particle-hole excitations remain strongly coupled with each other across the entire Fermi surface. In this case, even the observables that are local in the momentum space (such as the Green's functions) become dependent on the size of the Fermi surface in singular ways, resulting in a ultraviolet/infrared (UV/IR) mixing. By tuning the dimension and codimension of the Fermi surface independently, we find perturbative non-Fermi-liquid fixed points controlled by both UV/IR mixing and interactions.

arXiv:1407.0033•Physical Review B•Jul 24, 2015•74 citations

Bosonization of Fermi liquids

Jürg Martin Fröhlich, R. Götschmann

We consider systems of nonrelativistic, interacting electrons at finite density and zero temperature in d=2,3,ldots dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi-liquid (LFL) renormalization-group fixed point. We are especially interested in understanding under what circumstances such a system is a marginal Fermi-liquid (MFL) when the dimension of space is d\ensuremath{\geqslant}2. The interacting electron system is analyzed by combining renormalization-group (RG) methods with so called 'Luther-Haldane' bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ , which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant ${\mathrm{g}}_{\ensuremath{\lambda}}$ , which measures the strength of electron interactions at energy scales \ensuremath{\sim}${\mathrm{v}}_{\mathrm{F}}$ ${\mathrm{k}}_{\mathrm{F}}$ /\ensuremath{\lambda}. For systems with a strictly convex Fermi surface, superconductivity is the only symmetry-breaking instability. Excluding such an instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions, a deviation from LFL behavior is possible: if the exponent \ensuremath{\alpha} parametrizing the singularity of the interaction potential in momentum space by V-hat(|p|)\ensuremath{\sim}1/|p${\mathrm{|}}^{\mathrm{\ensuremath{\alpha}}}$ is greater than or equal to d-1, the results of the bosonization calculation are consistent with a MFL.

Physical review. B, Condensed matter•Mar 15, 1997•22 citations

Bosonization of Fermi Liquids

Froehlich, Juerg, Roland Goetschmann

We consider systems of non-relativistic, interacting electrons at finite density and zero temperature in d = 2, 3, ... dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi liquid (LFL) renormalization group fixed point. We are especially interested in understanding under what circumstances such a system is a Marginal Fermi liquid (MFL) when the dimension of space is greater or equal than 2 . The interacting electron system is analyzed by combining renormalization group (RG) methods with bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter, $λ^{-1} ,$ which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant, $ g_λ, $ which measures the strength of electron interactions at corresponding energy scales. Excluding a superconducting instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of $ λ^{-1} $ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions a deviation from LFL behaviour is possible : the results of the bosonization calculation are consistent with a MFL, if the exponent parametrizing the singularity of the interaction potential in momentum space is greater than or equal to d-1.

arXiv:cond-mat/9606100•Jun 14, 1996•0 citations

Bosonization of Fermi liquids

Roland Goetschmann

We consider systems of nonrelativistic, interacting electrons at finite density and zero temperature in d=2,3,ldots dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi-liquid (LFL) renormalization-group fixed point. We are especially interested in understanding under what circumstances such a system is a marginal Fermi-liquid (MFL) when the dimension of space is d\ensuremath{\geqslant}2. The interacting electron system is analyzed by combining renormalization-group (RG) methods with so called 'Luther-Haldane' bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ , which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant ${\mathrm{g}}_{\ensuremath{\lambda}}$ , which measures the strength of electron interactions at energy scales \ensuremath{\sim}${\mathrm{v}}_{\mathrm{F}}$ ${\mathrm{k}}_{\mathrm{F}}$ /\ensuremath{\lambda}. For systems with a strictly convex Fermi surface, superconductivity is the only symmetry-breaking instability. Excluding such an instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions, a deviation from LFL behavior is possible: if the exponent \ensuremath{\alpha} parametrizing the singularity of the interaction potential in momentum space by V-hat(|p|)\ensuremath{\sim}1/|p${\mathrm{|}}^{\mathrm{\ensuremath{\alpha}}}$ is greater than or equal to d-1, the results of the bosonization calculation are consistent with a MFL.

•Jan 1, 1996•4 citations

MARGINAL FERMI LIQUID WITH A TWO-DIMENSIONAL PATCHED FERMI SURFACE

A. FERRAZ, T. SAIKAWA, Z. Y. WENG

We consider a model composed of Landau quasiparticle states with patched Fermi surfaces (FS) sandwiched by states with flat FS to simulate the "cold" spot regions in cuprates. We calculate the one-particle irreducible function and the self-energy up to two-loop order. Using renormalization group arguments, we show that in the forward scattering channel, the renormalized coupling constant is never infrared stable due to the flat FS sectors. Furthemore, we show that the self-energy scales with energy as Re ∑~ω ln ω as ω→0, and thus the Fermi liquid state within each FS patch is turned into a marginal Fermi liquid.

arXiv:cond-mat/9908111•Modern Physics Letters B•Dec 30, 1999•4 citations
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.
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.
We study low-energy effective-field theories for non-Fermi liquids with Fermi surfaces of general dimensions and codimensions. When the dimension of the Fermi surface is greater than one, low-energy particle-hole excitations remain strongly coupled with each other across the entire Fermi surface. In this case, even the observables that are local in the momentum space (such as the Green's functions) become dependent on the size of the Fermi surface in singular ways, resulting in a ultraviolet/infrared (UV/IR) mixing. By tuning the dimension and codimension of the Fermi surface independently, we find perturbative non-Fermi-liquid fixed points controlled by both UV/IR mixing and interactions.
We consider systems of nonrelativistic, interacting electrons at finite density and zero temperature in d=2,3,ldots dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi-liquid (LFL) renormalization-group fixed point. We are especially interested in understanding under what circumstances such a system is a marginal Fermi-liquid (MFL) when the dimension of space is d\ensuremath{\geqslant}2. The interacting electron system is analyzed by combining renormalization-group (RG) methods with so called 'Luther-Haldane' bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ , which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant ${\mathrm{g}}_{\ensuremath{\lambda}}$ , which measures the strength of electron interactions at energy scales \ensuremath{\sim}vF{\mathrm{v}}_{\mathrm{F}}vF​ kF{\mathrm{k}}_{\mathrm{F}}kF​ /\ensuremath{\lambda}. For systems with a strictly convex Fermi surface, superconductivity is the only symmetry-breaking instability. Excluding such an instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions, a deviation from LFL behavior is possible: if the exponent \ensuremath{\alpha} parametrizing the singularity of the interaction potential in momentum space by V-hat(|p|)\ensuremath{\sim}1/|p${\mathrm{|}}^{\mathrm{\ensuremath{\alpha}}}$ is greater than or equal to d-1, the results of the bosonization calculation are consistent with a MFL.
We consider systems of non-relativistic, interacting electrons at finite density and zero temperature in d = 2, 3, ... dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi liquid (LFL) renormalization group fixed point. We are especially interested in understanding under what circumstances such a system is a Marginal Fermi liquid (MFL) when the dimension of space is greater or equal than 2 . The interacting electron system is analyzed by combining renormalization group (RG) methods with bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter, λ−1,λ^{-1} ,λ−1, which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant, $ g_λ, $ which measures the strength of electron interactions at corresponding energy scales. Excluding a superconducting instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of $ λ^{-1} $ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions a deviation from LFL behaviour is possible : the results of the bosonization calculation are consistent with a MFL, if the exponent parametrizing the singularity of the interaction potential in momentum space is greater than or equal to d-1.
We consider systems of nonrelativistic, interacting electrons at finite density and zero temperature in d=2,3,ldots dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi-liquid (LFL) renormalization-group fixed point. We are especially interested in understanding under what circumstances such a system is a marginal Fermi-liquid (MFL) when the dimension of space is d\ensuremath{\geqslant}2. The interacting electron system is analyzed by combining renormalization-group (RG) methods with so called 'Luther-Haldane' bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ , which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant ${\mathrm{g}}_{\ensuremath{\lambda}}$ , which measures the strength of electron interactions at energy scales \ensuremath{\sim}vF{\mathrm{v}}_{\mathrm{F}}vF​ kF{\mathrm{k}}_{\mathrm{F}}kF​ /\ensuremath{\lambda}. For systems with a strictly convex Fermi surface, superconductivity is the only symmetry-breaking instability. Excluding such an instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions, a deviation from LFL behavior is possible: if the exponent \ensuremath{\alpha} parametrizing the singularity of the interaction potential in momentum space by V-hat(|p|)\ensuremath{\sim}1/|p${\mathrm{|}}^{\mathrm{\ensuremath{\alpha}}}$ is greater than or equal to d-1, the results of the bosonization calculation are consistent with a MFL.
We consider a model composed of Landau quasiparticle states with patched Fermi surfaces (FS) sandwiched by states with flat FS to simulate the "cold" spot regions in cuprates. We calculate the one-particle irreducible function and the self-energy up to two-loop order. Using renormalization group arguments, we show that in the forward scattering channel, the renormalized coupling constant is never infrared stable due to the flat FS sectors. Furthemore, we show that the self-energy scales with energy as Re ∑~ω ln ω as ω→0, and thus the Fermi liquid state within each FS patch is turned into a marginal Fermi liquid.