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arXiv · 2206.13547

Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model

Erick Arguello Cruz·Grigory Tarnopolsky
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Abstract

We solve numerically the large $N$ Dyson-Schwinger equations for the Sachdev-Ye-Kitaev (SYK) model utilizing the Legendre polynomial decomposition and reaching $10^{-36}$ accuracy. Using this we compute the energy of the SYK model at low temperatures $T\ll J$ and obtain its series expansion up to $T^{7.54}$. While it was suggested that the expansion contains terms $T^{3.77}$ and $T^{5.68}$, we find that the first non-integer power of temperature is $T^{6.54}$, which comes from the two point function of the fermion bilinear operator $O_{h_{1}}=\chi \partial_{\tau}^{3}\chi$ with scaling dimension $h_{1}\approx 3.77$. The coefficient in front of $T^{6.54}$ term agrees well with the prediction of the conformal perturbation theory. We conclude that the conformal perturbation theory appears to work even though the SYK model is not strictly conformal.

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Erick Arguello Cruz, Grigory Tarnopolsky. 2022-06-27. Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model. https://doi.org/10.1103/physrevb.108.035103

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