Sachdev–Ye–Kitaev model as Liouville quantum mechanics

Dmitry Bagrets, Alexander Altland, Alex Kamenev

Research output: Contribution to journalArticle

117 Scopus citations


We show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝τ−3/2 for times larger than the inverse single particle level spacing τ≫Nln⁡N. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ϵ1/2. We also present exact diagonalization study supporting our conclusions.

Original languageEnglish (US)
Pages (from-to)191-205
Number of pages15
JournalNuclear Physics B
StatePublished - Oct 1 2016

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