Excitation spectra of quantum matter without quasiparticles I: Sachdev-Ye-Kitaev models

Understand

We study the low frequency spectra of complex Sachdev-Ye-Kitaev (SYK) models at general densities.

• The analysis applies also to 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 ($\omega$) axis at zero temperature ($T$).
• The asymptotic low $\omega$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states.