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 non-analytic 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 $N/M$.