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

TL;DR

This paper investigates the low-frequency excitation spectra of Sachdev-Ye-Kitaev models and SU(M) magnets, revealing universal behaviors and connections to holographic duality, with implications for understanding quantum matter without quasiparticles.

Contribution

It provides a detailed numerical analysis of the spectral densities of SYK models and SU(M) magnets, confirming their low-frequency scaling and identifying universal spectral features.

Findings

Low-frequency spectral densities match scaling dimensions of irrelevant operators.

Universal spin spectral weight computed for SU(M) magnets.

Reparameterization mode contributes to the spectral weight, linked to holographic duality.

Abstract

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. Of possible experimental interest is our computation of the universal spin spectral weight of the SU($M$) magnets at low $\omega$ and $T$: this includes a contribution from the time reparameterization mode, which is the boundary graviton of the holographic dual. This analysis is extended to a random $t$-$J$ model in a companion paper.