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

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 (\(\ome...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Tikhanovskaya, Maria, Guo, Haoyu, Sachdev, Subir, Tarnopolsky, Grigory
Format: Article
Language:English
Subjects:
Elementary excitations
Excitation spectra
Frequency spectrum
Gravitons
Magnets
Numerical analysis
Saddle points
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2010.09742