Excitation spectra of quantum matter without quasiparticles. I. Sachdev-Ye-Kitaev models
Maria Tikhanovskaya, Haoyu Guo, Subir Sachdev, Grigory Tarnopolsky
Abstract
We study the low-frequency spectra of complex Sachdev-Ye-Kitaev models at general densities. The analysis applies also to $\mathrm{SU}(M)$ magnets with random exchange at large $M$. The spectral densities are computed by numerical analysis of the saddle-point equations on the real frequency $\ensuremath{\omega}$ axis at zero temperature $T$. The asymptotic low-$\ensuremath{\omega}$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. Of possible experimental interest is our computation of the universal spin spectral weight of the $\mathrm{SU}(M)$ magnets at low $\ensuremath{\omega}$ and $T$; this includes a contribution from the time reparametrization mode, which is the boundary graviton of the holographic dual. This analysis is extended to a random $t\ensuremath{-}J$ model in the following paper [M. Tikhanovskaya et al., following paper, Phys. Rev. B 103, 075142 (2021)].