Abstract

We study a description of the large N limit of the Sachdev–Ye–Kitaev (SYK) model in terms of quantum mechanics without quenched disorder. Instead of random couplings, we introduce massive scalar fields coupled to fermions, and study a small mass limit of the theory. We show that, under a certain condition, the correlation functions of fermions reproduce those of the SYK model with a temperature dependent coupling constant in the large N limit. We also discuss a supersymmetric generalization of our quantum mechanical model. As a byproduct, we develop an efficient way of estimating the large N behavior of correlators in the SYK model.

Highlights

  • We study a description of the large N limit of the Sachdev-Ye-Kitaev (SYK) model in terms of quantum mechanics without quenched disorder

  • We show that our model reproduces essentially the large N limit of the SYK model, J should be replaced by a temperature dependent coupling Jeff

  • The simple replacement by the harmonic oscillators behaves as the Gaussian quenched disorder due to some special properties of the large N limit of the SYK model

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Summary

A Note on Sachdev-Ye-Kitaev Like Model without Random Coupling

Under a certain condition, the correlation functions of fermions reproduce those of the SYK model with a temperature dependent coupling constant in the large N limit. We show that our model reproduces essentially the large N limit of the SYK model, J should be replaced by a temperature dependent coupling Jeff .4. The large N behavior of the two and four point correlators of the SYK model are reproduced by our model. The simple replacement by the harmonic oscillators behaves as the Gaussian quenched disorder due to some special properties of the large N limit of the SYK model.

SYK model
Our model
Correlation function
Eight-point correlation function
Finite temperature
Relations to other models
SUSY generalization

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