What question did this study set out to answer?

To determine the analytical structure of the fermionic self-energy at finite temperature and frequency in canonical and noncanonical Fermi liquids at the first Matsubara frequency.

October 19, 2012Physical Review BOpen Access

First-Matsubara-frequency rule in a Fermi liquid. I. Fermionic self-energy

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Authors

ACAndrey V. ChubukovUniversity of Minnesota DMDmitrii L. MaslovUniversité Paris-Sud

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Implication

Theoretical analysis reveals strict self-energy constraints at the first Matsubara frequency in Fermi liquids, highlighting universal bounds for scaling forms in quantum data.

Key Points

To determine the analytical structure of the fermionic self-energy at finite temperature and frequency in canonical and noncanonical Fermi liquids at the first Matsubara frequency.
Analyzed the retarded fermionic self-energy across spatial dimensions D > 2 and 1 < D ≤ 2.
Evaluated self-energy behavior at the first Matsubara frequency (ω = iπT) using fully renormalized forward and backward scattering amplitudes.
Applied the local approximation near a Pomeranchuk instability to evaluate interaction vertices on the Fermi surface.
Demonstrated that for any dimension D > 1, the subleading term beyond O(T) in the self-energy at ω = iπT scales as T^D (or T^3 ln T in D = 3) and originates purely from forward and backward scattering.
Showed that the prefactor of the T^D term vanishes in the local approximation, eliminating all terms beyond O(T).
Identified two universal scaling constraints: substituting ω with iπT forces the imaginary part of self-energy to vanish and reduces the real part strictly to O(T).

Cite This Study

Chubukov et al. (2012) studied this question.

synapsesocial.com/papers/6a9079b2dfe186ac2f0d2991 https://doi.org/10.1103/physrevb.86.155136

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Implication

Theoretical analysis reveals strict self-energy constraints at the first Matsubara frequency in Fermi liquids, highlighting universal bounds for scaling forms in quantum data.

First-Matsubara-frequency rule in a Fermi liquid. I. Fermionic self-energy

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Implication

Key Points

Cite This Study

First-Matsubara-frequency rule in a Fermi liquid. I. Fermionic self-energy

Discussion

Member takes

Implication

Key Points

Cite This Study

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