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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Anomalous dimensions and the multiplicative renormalization group

G. Foegács

Published Aug 1, 1974• 1 citation
Publisher
DOI
10.1007/bf02742600

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Using a functional renormalization group approach we derive the renormalization group (RG) flow of a dissipative variant of the Yukawa-Sachdev-Ye-Kitaev model describing NNN fermions on a quantum dot, which interact via a disorder-induced Yukawa coupling with MMM bosons. The inverse Euclidean propagator of the bosons is assumed to exhibit a nonanalytic term proportional to the modulus of the Matsubara frequency. We show that, to leading order in 1/N1/N1/N and 1/M1/M1/M, the hierarchy of formally exact flow equations for the irreducible vertices of the disorder-averaged model can be closed at the level of the two-point vertices. We find that the RG flow exhibits a non-Fermi liquid fixed point characterized by a finite fermionic anomalous dimension $\ensuremath{\eta}$, which is related to the bosonic anomalous dimension $\ensuremath{\gamma}$ via the scaling law $2=2\ensuremath{\eta}+\ensuremath{\gamma}$ with $0<\ensuremath{\eta}<1/2$. We explicitly calculate $\ensuremath{\eta}$ and the critical exponents characterizing the linearized RG flow in the vicinity of the fixed point as functions of N/MN/MN/M.