Non-Fermi liquid fixed point of the dissipative Yukawa-Sachdev-Ye-Kitaev model

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 N fermions on a quantum dot, which interact via a disorder-induced Yukawa coupling with M 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/N and 1/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 eta, which is related to the bosonic anomalous dimension gamma via the scaling law 2 = 2 eta + gamma with 0 < eta < 1/2. We explicitly calculate eta and the critical exponents characterizing the linearized RG flow in the vicinity of the fixed point as functions of N/M.