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

Erick Arguello CruzGrigory Tarnopolsky
Jun 2022
摘要
We solve numerically the large $N$ Dyson-Schwinger equations for theSachdev-Ye-Kitaev (SYK) model utilizing the Legendre polynomial decompositionand reaching $10^{-36}$ accuracy. Using this we compute the energy of the SYKmodel 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 bilinearoperator $O_{h_{1}}=\chi \partial_{\tau}^{3}\chi$ with scaling dimension$h_{1}\approx 3.77$. The coefficient in front of $T^{6.54}$ term agrees wellwith the prediction of the conformal perturbation theory. We conclude that theconformal perturbation theory appears to work even though the SYK model is notstrictly conformal.
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