Resonant level model coupled to a Sachdev-Ye-Kitaev bath

Abstract

We investigate the non-equilibrium dynamics of a resonant level model coupled to a strongly interacting electron bath modeled by a Sachdev-Ye-Kitaev (SYK) model. Different from the well-investigated case of a structureless non-interacting Fermi gas bath leading to a temperature-independent exponential decay of the impurity orbital occupation, we find a temperature-dependent oscillatory decay. We attribute this difference to the lack of quasiparticles in the SYK model, which is reflected in its singular density of states at the Fermi level. Our results are exact and can be obtained analytically by mapping to a suitably structured Fermi gas bath as an ancillary model for the SYK bath.

Figures (3)

• Figure 1: Comparison of different bath models.
• Figure 2: Top row: Density of states of the SYK bath $\rho_c(\omega)$ (left) and the impurity $\rho_d(\omega)$ for $q = 4, 8, 16$ (right) for zero temperature. Notice the divergence $\propto |\omega|^{-1+2/q}$ for the SYK bath and the non-analytic suppression $\propto |\omega|^{1-2/q}$ for the local impurity density of states at the Fermi energy. Bottom row: Density of states of the SYK-4 bath (left) and the impurity (right) for non-zero temperature. Notice that the behavior at the Fermi energy becomes analytic for non-zero temperature. The plots are scaled with the characteristic energy scales $J$ and $\omega_0$ (eq. (\ref{['scaling']})) for the SYK bath and the impurity, respectively, and show the universal behavior as a function of these energy scales.
• Figure 3: Impurity occupation as a function of time after a quench coupling to (a) SYK-2 bath, (b) SYK-4 bath, (c) SYK-16 bath. All curves are universal functions of the energy scale $\omega_0$ from (\ref{['scaling']}).